Abstracts book ismn-2015

International Conference

Interaction ofSuperconductivity and Magnetismin Nanosystems

book of abstracts

2–4 September, 2015Moscow, Russia

http://www.misis.ru

http://www.misis.ru

Title: International Conference “Interaction of Superconductivity and Magnetismin Nanosystems”

Published on August 2015by Multiprint (ООО ”ПКЦ АЛЬТЕКС”), Moscow, Russia

Conference web-site:http://science.misis.ru/en/activity/nanosystem

© 2015 Multiprint

© 2015 Authors

ISBN 978-5-93121-375-0

Book contains abstracts presented at the conference in Moscow, Sep 2-4,2015. Conference is organized by National University of Science and Technology“MISIS”. Org. committee:

• Chairman: Prof. Konstantin Efetov, NUST “MISIS” (Russia) and Ruhr Uni-versity Bochum (Germany)

• Vice chairman: Prof. Valery Ryazanov, NUST “MISIS” (Russia) and ISSPRAS (Russia)

• Vice chairman: Prof. Sergei Mukhin, NUST “MISIS” (Russia)• Karpov A.V.• Shitov S.V.• Ustinov A.V.• Chernikov M.A.• Kheyfets B.B.• Galimzyanov T.R.• Smirnova E.A.• Maleeva N.A.• Shtanskaya E.V.• Lebedeva E.A.• Chernykh S.V.

http://science.misis.ru/en/activity/nanosystem

Program Overview2 September, room B-49:30 Registration of participants

10:00 Plenary Session: Collective Phenomena …11:20 Cofee Break11:40 Plenary Session14:00 Lunch15:00 High- superconductors … Superconducting Spin Valves …↓ ↓

B-4 B-317:30 Cofee Break17:40 Poster session (B-building, 2nd loor hall)18:45 End of conference day

3 September, room B-49:30 Plenary Session: Collective Phenomena …

11:30 Cofee Break11:50 Plenary Session14:10 Lunch15:10 Triplet superconductivity … Hybrid superconducting …↓ ↓

B-4 B-318:20 End of conference day

4 September, room B-49:30 Plenary Session: Hybrid Systems …

11:20 Cofee Break11:40 Plenary Session14:00 Lunch15:00 Plenary Session17:00 Closing Conference17:15 Cofee Break17:35 Meeting with faculty and students (B-702 and B-725)

Program OverviewProgram

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2 September, room: B-4Plenary Session: Collective Phenomena in QuantumMatter

chairman: Prof. Konstantin Efetov9:30 Registration of participants

10:00 Strange Metals, Fermion Signs and EntanglementJan ZaanenInstituut Lorentz for Theoretical Physics, Leiden University, The NetherlandsAbstract: see page 60

10:40 Strongly Correlated Electrons in High Temperature SuperconductorsAlvaro FerrazInternational Institute of Physics-UFRN, BrazilAbstract: see page 25

11:20 Cofee Break

chairman: Prof. Sergei Mukhin

11:40 Cascade of Phase Transitions Near Quantum Critical PointKonstantin EfetovRuhr University Bochum, Germany; National University of Science and Technol-ogy MISIS, Moscow, RussiaAbstract: see page 23

12:20 Time-Reversal Broken Chiral Superconducting Phase Driven by Electronic Corre-lations in TiSe2Dmitry EfremovLeibniz Institute for Solid State and Materials Research, Dresden, GermanyAbstract: see page 24

13:00 Quasi-Fermi Liquid: a Special State of One-Dimensional MatterAlexander RozhkovITAE RAN, Moscow, Russia; MIPT, Dolgoprudnyi, RussiaAbstract: see page 46

13:30 Three Component Spin-Charge Superconducting Order Parameter and Pair Den-sity Waves in Correlated Fermi Systems in a Magnetic FieldSergei MatveenkoLandau Institute for Theoretical Physics, MoscowAbstract: see page 38

14:00 Lunch

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2 September, room: B-4High-Temperature Superconductors chairman: Prof. Jan Zaanen

15:00 Efect of Van Hove Singularities on the d-Form Factor Charge Ordering in CuprateHigh-Temperature SuperconductorsPavel VolkovRuhr University Bochum, GermanyAbstract: see page 58

15:30 SnS-Andreev Spectroscopy of Fe-based Oxypnictides: Scaling of SuperconductingParameters with �Tatiana KuzmichevaLebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia;Lomonosov Moscow State University, 119991 Moscow, RussiaAbstract: see page 35

16:00 Paramagnon Excitations Theory for Magnetic Properties of Layered Copper OxideSuperconductorsIgor LarionovNational University of Science & Technology ”MISIS”, 119049, Moscow, Russia;Kazan Federal University, 420008, Kremlevskaya, 18, Kazan, RussiaAbstract: see page 36

16:30 Modeling of Intrinsic Josephson Junctions in High Temperature SuperconductorsYury ShukrinovBLTP, Joint Institute for Nuclear Research, and Dubna International University ofNature, Society, and Man, Dubna, RussiaAbstract: see page 50

17:00 Charge Imbalance in a Stack of Intrinsic Josephson Junctions Under External Ra-diationMajed NashaatDepartment of Physics, Faculty of Science, Cairo University, EgyptAbstract: see page 42

17:30 Cofee Break

2 September, room: B-4Program

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2 September, room: B-3Superconducting Spin-Valves chairman: Prof. Valery Ryazanov

15:00 Distribution of Condensate Functions in Superconducting Spin-ValvesLenar TagirovKazan Federal University, Kazan, RussiaAbstract: see page 55

15:40 FSF Spin-Valves: Comparison of Diferent ModelsNataliya PugachSkobeltsyn Institute of Nuclear Physics, MSU, MoscowAbstract: see page 43

16:10 Controllable Tuning of Spin-Singlet and Spin-Triplet Currents in a Josephson Spin-ValveVladimir KrasnovStockholm University, AlbaNova University Center, SE-10691 Stockholm, SwedenAbstract: see page 32

16:50 Exchange Biasing of Diluted Ferromagnetic Alloy Films in Superconducting Spin-ValvesAnatolie SidorenkoD. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM,MD2028 Kishinev, MoldovaAbstract: see page 51

17:30 Cofee Break


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2 September, B-building: Hall of 2nd

FloorPoster SessionThe poster session is going to be from 17:40 to 18.45. List of poster reports:

• Imaging Coherent Response of a Superconducting Metasurface

Alexander AverkinNational University of Science and Technology (MISIS), Leninskiy prosp. 4, 119049Moscow, Russia

Abstract: see page 15

• Superconducting Proximity Efect in Multiorbital Materials with Strong Spin-Orbital Cou-pling

Angelina Burmistrova

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics,Moscow, Russian Federation; Lomonosov Moscow State University, Faculty ofPhysics, Moscow, Russian Federation; Moscow State Pedagogical University,Moscow, Russian Federation


• Novel Nb/Pd0.99Fe0.01/Nb Josephson Junction Magnetic Switches for Cryogenic Memory

Igor Golovchanskiy

National University of Science and Technology MISIS, Moscow, Russia; Moscow In-stitute of Physics and Technology, Dolgoprudny, Moscow Region, Russia


• Anomalous Proximity Efect and More Than One Majorana Fermion

Satoshi Ikegaya

Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan


• Dielectric Susceptibility of Magnetoelectric Thin Films with Vortex-Antivortex Dipole Pairs

Petr Karpov

Department of Theoretical Physics and Quantum Technologies, National Universityof Science and Technology MISiS, Leninski avenue 4, 119049, Moscow, Russia


2 September, B-building: Hall of 2nd FloorProgram

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• Peculiarity of Resonance Between Fluxon and Plasma Wave in One-Dimensional Parallel Arrayof Josephson Junctions

Kirill Rodin

Dubna International University of Nature, Society, and Man, Dubna, Russia


• Detection of Single Abrikosov Vortex in a Microwave Superconductor Resonator

Kirill Shulga

National University of Science and Technology (MISIS), Moscow, Russia; RussianQuantum Center, Skolkovo, Russia; Moscow Institute of Physics and Technology,Dolgoprudny, Russia


• Electrical Conduction in YBa2Cu3O7–δ Single Crystals Under the Conditions of Anionic Or-dering in the Cu(1) O1–δ Layers

Nikolai Sobolev

Departamento de Física and I3N, Universidade de Aveiro, Aveiro, Portugal; NationalUniversity of Science and Technology “MISiS”, Moscow, Russia


• Vortices at the Surface of a Normal Metal Coupled by Proximity Efect to a Superconductor

Vasiliy Stolyarov

Institut des Nanosciences de Paris, UPMC and CNRS-UMR 7588, Paris, France;Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Institute of SolidState Physics RAS, Chernogolovka, Moscow region, Russia


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chairman: Prof. Alvaro Ferraz9:30 High- and Low Superconductivity and Superluidity in Fermi-Systems with

RepulsionMaxim KaganP.L. Kapitza Institute for Physical Problems, RAS, MoscowAbstract: see page 29

10:10 Geometrically Controlled Quantum Coherence and Non-Equilibrium Efects inNanoscopic Kondo DropletsDirk MorrUniversity of Illinois at Chicago, USAAbstract: see page 40

10:50 Fluctuations of “Hidden Order” as Cooper Pairing GlueSergei MukhinMoscow Institute for Steel and Alloys, Moscow, RussiaAbstract: see page 41

11:30 Cofee Break


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chairman: Prof. Lenar Tagirov

11:50 Clustering of Vortex Matter in Superconductor-Ferromagnet MetamaterialsAlexander BuzdinUniversity of Bordeaux, LOMA UMR-CNRS 5798, F-33405 Talence Cedex, FranceAbstract: see page 20

12:30 Microscopic Theory of Vortex Pinning on Columnar Defects in Conventional, Chi-ral and Ferromagnetic SuperconductorsAlexander Mel’nikovInstitute for Physics of Microstructures, Russian Academy of Sciences, 603950Nizhny Novgorod, GSP-105, Russia; Lobachevsky State University of NizhnyNovgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, RussiaAbstract: see page 38

13:10 Long-Range Spin Signal in Mesoscopic Structures Under a Zeeman SplittingIrina BobkovaInstitute of Solid State Physics, RASAbstract: see page 17

13:40 Fluxon Scattering as a Tool for Detection and Manipulations with Flux QubitStatesIgor SolovievLomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics,Moscow, Russia Lukin Scientiic Research Institute of Physical Problems, Ze-lenograd, Moscow, Russia MIPT, State University, Dolgoprudniy, RussiaAbstract: see page 53

14:10 Lunch


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3 September, room: B-4Triplet Superconductivity and Current-Phase Relationin Superconductor-Ferromagnet Systems

chairman: Prof. Alexander Buzdin15:10 Interference of Triplet -wave Condensates in Coupled Josephson Junctions

Andreas MoorRuhr-Universität Bochum, GermanyAbstract: see page 40

15:50 Triplet Proximity Efect in Superconducting Heterostructures with a Half-MetallicLayerSergey MironovUniversity Bordeaux, Talence Cedex, France; MIPT, Dolgoprudny, Russia; Insti-tute for Physics of Microstructures RAS, Nizhny Novgorod, RussiaAbstract: see page 39

16:20 Observation of the Second Fourier Component in the Current-Phase Relation ofJosephson SFS JunctionsVitaly BolginovISSP RAS; MISiSAbstract: see page 18

16:50 Long–Range Singlet Josephson Spin–Valve Efect in Ballistic SFS JunctionAlexey SamokhvalovInstitute for Physics of Microstructures RAS, GSP-105, Nizhny Novgorod, RussiaAbstract: see page 48

17:20 Superconducting Phase Domains in Thin s-layers of S-F/N-sIS Josephson DevicesSergey BakurskiyPhysics Department, MSU, 119991 Moscow, Russia; MIPT, Dolgoprudniy, RussiaAbstract: see page 16

17:50 Current Transport in SF-NFS Josephson Structures: Theory and ApplicationNikolay KlenovNIIFP, Zelenograd, Russia; Physics Department, MSU, RussiaAbstract: see page 31


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3 September, room: B-3Hybrid Superconducting Structures with TopologicalInsulators

chairman: Prof. Yasuhiro Asano15:10 Spectroscopy of Surface Andreev Bound States in Topological Insulator / Supercon-

ductor JunctionsAlexander GolubovFaculty of Science and Technology and MESA; Institute of Nanotechnology, Uni-versity of Twente, Netherlands; MIPT, Dolgoprudny, RussiaAbstract: see page 27

15:50 Majorana Fermions in Topological Insulator — Superconductor Heterostructure ina Magnetic FieldRamil AkzyanovMIPT, Dolgoprudny, Moscow Region, Russia; Institute for Theoretical and Ap-plied Electrodynamics, Moscow, Russia; All-Russia Research Institute of Auto-matics, Moscow, RussiaAbstract: see page 14

16:20 Coherent Electronic Transport in Hybrid Superconductor/Semiconductor-Nanowire StructuresIgor BatovPeter Gruenberg Institute, Forschungszentrum Juelich, Germany; ISSP,Chernogolovka, Russia; MIPT, Dolgoprudny, RussiaAbstract: see page 17

16:50 Josephson Junction Detectors for Majorana and Dirac FermionsMoitri MaitiBLTP, JINR, Dubna, RussiaAbstract: see page 37

17:20 Peculiarities of DC-SQUIDs with Topologically Nontrivial BarrierIlhom RahmonovBLTP, Joint Institute for Nuclear Research, Dubna, Russia; Umarov Physical andTechnical Institute, Dushanbe, TajikistanAbstract: see page 44


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4 September, room: B-4Plenary Session: Hybrid Systems: Superconductors inContact with Magnetic Materials, TopologicalInsulators, and Graphene

chairman: Prof. Alexander Mel’nikov9:30 Recent Topic in Odd-Frequency Pairing: Consequences of Bulk Odd-Frequency Su-

perconducting StatesYukio TanakaDepartment of Applied Physics, Nagoya University, Nagoya 464-8603, Japan;Moscow Institute of Physics and Technology, 141700 Dolgoprudny, RussiaAbstract: see page 56

10:10 Paramagnetic Response of Small Topological SuperconductorsYasuhiro AsanoDepartment of Applied Physics, Hokkaido University, Sapporo, 060-8628, JapanAbstract: see page 15

10:50 Specular Interband Andreev Relections in GrapheneDmitri EfetovMassachusets Institute of Technology, Cambridge, USAAbstract: see page 22

11:20 Cofee Break


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chairman: Prof. Alexander Golubov11:40 Doping Asymmetry of Superconductivity Coexisting with Antiferromagnetism in

Spin Fluctuation TheoryIlya EreminRuhr-Universität Bochum, Institut für Theoretische Physik, Bochum, GermanyAbstract: see page 24

12:20 The Microscopic Theory of a Normal and the Josephson Current in Junctions withMultiband and Topological SuperconductorsIgor DevyatovLomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, 1(2),Leninskie gory, GSP-1, Moscow Russian FederationAbstract: see page 21

12:50 Josephson Efect in SIFS Tunnel Junctions with Complex Barriers in Weak LinkRegionMikhail KupriyanovMoscow Institute of Physics and Technology, 141700 Dolgoprudniy, Russia; Sko-beltsyn Institute of Nuclear Physics, Lomonosov MSU, 119991 Moscow, Russia;Institute of Physics, Kazan (Volga region) Federal University, 420008 Kazan, Rus-siaAbstract: see page 33

13:30 Crossed Surface Flat Bands in Weyl Semimetal SuperconductorsKeiji YadaNagoya UniversityAbstract: see page 59

14:00 Lunch


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chairman: Prof. Mikhail Kupriyanov

15:00 Prospective Applications of Superconducting and Superconducting-FerromagneticHeterostructuresIgor VernikHYPRES, Inc., 175 Clearbrook Road, Elmsford, NY 10523, USAAbstract: see page 57

15:40 Escape and Retrapping in Josephson � JunctionsEdward GoldobinPhysikalische Institut, Experimentalphysik II, University of Tübingen, Tübingen,GermanyAbstract: see page 25

16:20 Superconducting Hybrids: From Sandwiches to Planar StructuresValery RyazanovInstitute of Solid State Physics, RAS, Chernogolovka, Moscow distr., Russia; Na-tional University of Science and Technology ”MISiS”, Moscow, RussiaAbstract: see page 47

17:00 Closing Conference

17:15 Cofee Break

17:35 Meeting with faculty and graduate students of Theoretical Physics andQuantum Technologies department (B-725) and Laboratory of Supercon-ducting Metamaterials (B-702)


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Majorana Fermions in Topological Insulator — SuperconductorHeterostructure in a Magnetic Field

Ramil Akzyanov1,2,3, A.L. Rakhmanov1,2,3, A.V. Rozhkov1,2, and A.D.Zabolotsky4,3

1: MIPT, Dolgoprudny, Moscow Region, Russia2: Institute for Theoretical and Applied Electrodynamics, Moscow, Russia

3: All-Russia Research Institute of Automatics, Moscow, Russia4: Institute for Spectroscopy, Moscow, Russia

Report time: see page 10; Contact e-mail: [email protected]

We investigate the superconducting proximity efect at the surface of topolog-ical insulator in the presence of magnetic ield. It is known that Majorana fermionexists at the vortex in topological insulator - superconductor heterostructure [1].In the presence of large Zeeman ield a topological phase transition occurs in thesystem and irst Chern number changes from 0 to 1. New phase has irst Chernnumber equal to 1, however, no Majorana fermion exists at the vortex core in suchphase. In this work orbital efects of magnetic ield have been studied in detail.It is shown that while one Majorana fermion is localized at the vortex core, thesecond, exterior, Majorana fermion is localized at the distance ∗ ∼ � ��, where�√ ℎ� is magnetic length and � is the coherence length at the surface of topolog-ical insulator. At suiciently large magnetic ield ∼ � exterior Majorana fermionis localized near the vortex and is combined with vortex Majorana fermion intothe state with nonzero energy. Realistic setup of superconducting island placedon the top of topological insulator has been studied. If vortex penetrates the is-land, one Majorana fermion is localized at the vortex core while the second Majo-rana fermion is localized at the edge of the island. We found that the energy gapbetween edge Majorana fermion and the irst excited state is of the order of super-conducting gap induced at the surface of the topological insulator if the systemparameters are optimized. Such Majorana fermion can be observed in scanningtunneling microscope measurement.

References:1. L. Fu and C.L. Kane, 100, 096407 (2008).

Paramagnetic Response of Small Topological SuperconductorsYasuhiro Asano and Shu-Ichiro Suzuki

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[email protected]

Department of Applied Physics, Hokkaido University, Sapporo, 060-8628, Japan


The diamagnetism is an essential property of all superconductors. However,we will show that small topological (or unconventional) superconductors canbe intrinsically paramagnetic at very low temperature by solving the quasiclas-sical Eilenberger equation and the Maxwell equation self-consistently on two-dimensional superconducting disks in weak magnetic ields. Because of the topo-logically nontrivial character of the wave function, the unconventional supercon-ductors host the zero-energy surface Andreev bound states, which always accom-pany so-called odd-frequency Cooper pairs. The paramagnetic property of theodd-frequency pairs explains the paramagnetic response of the disks at low tem-perature. We also discuss efects of rough edge at the disc surface. In a d-wave su-perconducting disc, the paramagnetic response is fragile in the presence of roughsurface because the paramagnetic odd-frequency pairs have the p-wave orbitalsymmetry. On the other hand in a p-wave disc, the paramagnetic efect is ro-bust against the surface roughness because the odd-frequency pairs have s-waveorbital symmetry. Thus the paramagnetic response is characteristic feature of asmall spin-triplet superconductor.

References:1. S.-I. Suzuki and Y. Asano, Phys. Rev. B 89, 184508 (2014).2. S.-I. Suzuki and Y. Asano, Phys. Rev. B 91, in press.

Imaging Coherent Response of a Superconducting MetasurfaceAlexander Averkin1, A. Zhuravel2 , P. Jung5, N. Maleeva1, V. P. Koshelets3, L. V.

Filippenko3, A. Karpov1, and A. V. Ustinov1,4,51: National University of Science and Technology “MISIS”, Moscow, Russia

2: B. Verkin Institute for Low Temp. Physics and Engineering, NAS of Ukraine, Kharkov,Ukraine

3: Kotel’nikov Institute of Radio Engineering and Electronics, Moscow Russia4: Russian Quantum Center (RQC), Skolkovo, Moscow region, Russia

5: Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany


We study microwave response of the individual meta-atoms of a supercon-ducting metasurface formed by a two-dimensional array of SuperconductingQUantum Interference Devices (SQUIDs). In our experiment, RF currents in the

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[email protected]

metasurface are directly imaged by using Laser Scanning Microscopy (LSM) tech-nique. We tested a sample with 21×21 SQUID array in a waveguide cavity de-signed to achieve a uniform microwave distribution over the entire array. Thedemonstrated tunability of 2D SQUID metasurface resonance frequency by ex-ternal magnetic ield is about ��%, covering 8 − �� GHz range. The obtainedLSM images of the RF current distributions over the SQUID array conirm a highdegree of coherence of the entire metasurface.

Superconducting Phase Domains in Thin s-layers of S-F/N-sISJosephson Devices

Sergey Bakurskiy1,2, A.A.Golubov2,3, N.V.Klenov1, M.Yu.Kupriyanov4,5, I. I.Soloviev4

1: Physics Department, MSU, 119991 Moscow, Russia2: MIPT, Dolgoprudniy, Russia

3: Institute for Nanotechnology, University of Twente, Netherlands4: Skobeltsyn Institute of Nuclear Physics, MSU, Moscow, Russia

5: Institute of Physics, Kazan (Volga region) Federal University, Kazan, Russia


Josephson junctions containing normal (N) and ferromagnetic (F) materials inthe weak link region are currently the subject of intense research. The interest insuch structures is due to the possibility of their use as a control elements of super-conductor memory compatible with the RSFQ logic. At present there are manyimplementations of such controls. Among them, the tunnel structures containingone ferromagnetic layer in the weak link region are of greatest interest. Anisotropyof their properties necessary for operations is achieved in such devices by com-plicating the structure of the weak-coupling area.

In this work we study theoretically the properties of S-F/N-sIS tunnel devicesin the frame of the quasiclassical Usadel formalism. We assume that the scale ofthe structure is much less than the Josephson penetration depth. We demonstratethat in the S-F/N-sIS device it is possible to achieve its separation into two regionswhich have positive (0 segment) and negative (� segment) critical current densi-ties. We prove by numerical calculations that this separation is accompanied by anew phenomenon, namely the violation of a spatial uniformity of the supercon-ductive ilm and its decomposition into domains with an order parameter phasediference equal to π. The efect is sensitive to thickness of the s layer and widths

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of F and N ilms in the direction along the sIS interface and vanishes in the limitof thick s-electrode.

Coherent Electronic Transport in HybridSuperconductor/Semiconductor-Nanowire Structures

H.Y. Guenel1, Igor Batov1,2,3, N. Borgwardt1, H. Hardtdegen1, A. Winden1, K.Sladek1, G. Panaitov1, D. Gruetzmacher1, Th. Schaepers1

1: Peter Gruenberg Institute, Forschungszentrum Juelich, Germany2: ISSP, Chernogolovka, Russia3: MIPT, Dolgoprudny, Russia


We have fabricated and studied symmetric and asymmetric planar Josephsonjunctions based on InAs-nanowires and superconducting Nb-, Al- electrodes. Atlow bias current regime, the symmetric junctions exhibited a pronounced Joseph-son supercurrent. The critical current monotonously decreased with the magneticield, which can be explained by a recently developed theoretical model for theproximity efect in ultra-narrow Josephson junctions. The symmetric junctionsalso showed clear signatures of subharmonic gap structures. At zero magneticield, a Josephson coupling was found for the asymmetric Al/InAs-nanowire/Nbjunctions as well. By applying a magnetic ield above the critical ield of Al or byraising the temperature above the critical temperature of Al the junction couldbe switched to an efective single interface superconductor/nanowire structure.In this regime, a pronounced peak in the diferential conductance was observed,which is explained by relectionless tunneling.

References:1. H.Y. Guenel, N. Borgwardt, I.E. Batov et al. // Nano Lett. 14, 4977 (2014).2. H.Y. Guenel, I.E. Batov et al. // J. Appl. Phys. 112, 034316 (2012).

Long-Range Spin Signal in Mesoscopic Structures Under aZeeman Splitting

Irina Bobkova and A.M. BobkovInstitute of Solid State Physics, RAS


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[email protected]

A theory of spin transport and spin detection in Zeeman-splitted supercon-ducting ilms at low temperatures is developed. A new mechanism to create anonequilibrium spin signal, speciic only for Zeeman-splitted superconductors,is proposed [1,2,3]. In the framework of this mechanism the observed spin sig-nal is formed by the spin-independent nonequilibrium quasiparticle distributionweighted by the spin-split DOS. The relaxation length of such a spin signal is de-termined by the energy relaxation length and can be extremely large.

There can exist two types of signals: due to nonthermalized quasiparticle dis-tribution and due to thermalized overheated electron distribution. They have dif-ferent decay lengths and can be distinguished by their diferent dependencies onthe applied voltage.

The decay length of the nonthermalized signal is determined by the electron-electron scattering rate, renormalized due to superconductivity. It depends cru-cially on the temperature of the electron sybsystem and superconducting gap.The decay length of the thermalized signal is determined by the electron-phononrelaxation length and can be very large.

Applications of the theory to recent experimental data on spin relaxation inZeeman-splitted and exchange-splitted superconductors [4,5,6] are discussed. Inparticular, it can explain the extremely high spin relaxation lengths, experimen-tally observed in Zeeman-splitted superconductors, and their growth with themagnetic ield and with the applied voltage.

References:1. I.V. Bobkova and A.M. Bobkov, Pis’ma v ZhETF, 101, 124 (2015)2. T. Krishtop, M. Houzet, J. S. Meyer, PRB 91, 121407(R) (2015)3. M. Silaev, P. Virtanen, F.S. Bergeret, T.T. Heikkilä, PRL 114, 167002 (2015)4. F. Hubler, M.J. Wolf, D. Beckmann, and H.v. Lohneysen, Phys. Rev. Lett.

109, 207001 (2012); C.H.L. Quay, D. Chevallier, C. Bena, M. Aprili, NaturePhys. 9, 84 (2013)

5. M.J. Wolf, F. Hubler, S. Kolenda, H.v. Lohneysen, and D. Beckmann, Phys.Rev. B 87, 024517 (2013)

6. M.J. Wolf, C. Surgers, G. Fisher, and D. Beckmann, Phys. Rev. B 90 (2014)

Observation of the Second Fourier Component in theCurrent-Phase Relation of Josephson SFS Junctions

Vitaly BolginovISSP RAS; MISiS


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It is well known that the phase diference and the supercurrent through aJosephson junction are connected via odd ��-periodic relation. In particular casesthe current-phase relation (CPR) is sinusoidal one but in general it may containhigher harmonics of Fourier transformation. Josephson SFS junctions with ferro-magnetic barrier are of great interest due to oscillation of its critical current vs.barrier width caused by spin antagonism of ferromagnetism and superconduc-tivity. The F-barrier width increasing causes periodic change of critical currentsign, or more exactly, the change of the irst CPR Fourier component sign. Atnode points (� − � transitions) the amplitude of the irst CPR component turns tozero that enables an observation of higher Fourier components. For example, inthe node point one may observe such amazing efect as half periodic CPR due todomination of the second Fourier component.

Here I report a series of experiments that undoubtedly demonstrates the sec-ond CPR component manifestations. We studied Nb–CuNi–Nb SFS-sandwicheswith 53 at. % Ni content in the CuNi interlayer. We’ve observed that at node point(about 7 nm of the F-barrier width) the critical current temperature dependencehas shown a reentrant behavior with nonzero critical current at the �−� transitiontemperature. At this temperature one may observe half-integer Shapiro steps ap-pearance under inluence of ac-signal. Measurements of critical current vs. mag-netic ield curves have shown that the sample is uniform and the efect is not dueto the junction separation into 0- and �-state regions. Moreover at the transitiontemperature we could observe half-periodic Fraunhopher pattern that conirmsdomination of the second CPR Fourier component. Also we have carried out adirect measurement of the current-phase relation and demonstrated directly thepresence and domination of the second component in it. Some theoretical modelswill be given to discuss unexpectedly high value of the second harmonic ampli-tude.

Superconducting Proximity Efect in Multiorbital Materials withStrong Spin-Orbital Coupling

Angelina Burmistrova1,2,3, I.A. Devyatov11: Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, Moscow,

Russian Federation2: Lomonosov Moscow State University, Faculty of Physics, Moscow, Russian Federation

3: Moscow State Pedagogical University, Moscow, Russian Federation


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[email protected]

New microscopic tight-binding model for calculation of charge transport inheterostructures containing unusual multiband materials is proposed which al-lows to take into account multiband Fermi surface, the nonparabolic excitationspectrum of the considered materials and also interband and intervalley scatteringat the boundaries. This tight-binding approach has been applied to the investiga-tion of the proximity efect in heterostructures, containing materials with strongspin-orbit interaction and topological insulators (2D and 3D strained HgTe). In-duced superconducting order parameter in this material should not be treatedthe same as in the single-band metal due to its essentially multiband structureand the existence of the strong spin-orbital coupling. Taking into account mul-tiorbital structure and complex non-parabolic excitation spectrum in such inter-esting materials we have calculated the induced by usual s-wave superconductorexcitation spectrum in them and have obtained the efective 2D Hamiltonian. Thecalculations of the normal and Josephson current in structures containing metalswith strong spin-orbit interaction were performed using the obtained efective 2DHamiltonian.

Clustering of Vortex Matter in Superconductor-FerromagnetMetamaterials

Alexander Buzdina, A. Bespalova, A. Mel’nikovba: University of Bordeaux, LOMA UMR-CNRS 5798, F-33405 Talence Cedex, France

b: Institute for Physics of Microstructures RAS, and Lobachevsky State University, 603950Nizhny Novgorod, Russia


Metamaterials combining superconducting (S) and ferromagnetic (F) com-pounds permit to attend new functionalities and reveal unusual counterintuitiveefects. We show that the SF superlattices may display a very special electrody-namics due to the nonlocal polarization of the magnetic subsystem, making theintervortex interaction attractive at some distances [1]. These SF superlattices vio-late the standard classiication scheme based on the Ginzburg-Landau parameterκ the type-I and type-II superconductors correspond to � � ��√� and � � ��√�,respectively. In the SF superlattices the vortex matter can be arranged in clus-ters forming, thus, an intermediate state with alternating vortex and Meissnerphases. The physics of these clustering phenomenon is related to the modiica-tion of the intervortex interaction due to the nonlocal polarization of the magneticsubsystem. Tuning the parameters of the F and S subsystems one can engineer the

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phase diagram of the vortex matter in SF superlattices. Our study permits to pro-vide concrete recommendations for the proper choice of parameters for such S/Fmetamaterials.

Fig. 1

References:1. Bespalov, A. A., Mel’nikov, A. S. and Buzdin, A. I., EPL v. 110 (2015) 37003.

The Microscopic Theory of a Normal and the Josephson Currentin Junctions with Multiband and Topological Superconductors

Igor Devyatov1 and A.V. Burmistrova1,21: Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, 1(2),

Leninskie gory, GSP-1, Moscow Russian Federation2: Moscow State Pedagogical University, Moscow Russian Federation


We present a new microscopic tight-binding approach for calculation of chargetransport in junctions with multiband and topological superconductors [1,2]. Ourapproach takes into account the complex excitation spectrum of these supercon-ductors, their multiband Fermi surface, the anisotropy of the superconductingorder parameter as well as interband and intervalley scattering at the boundaries.This theory has been applied to calculations of a normal and the Josephson currentin diferent structures contained multiband Fe-based superconductors (FeBS). Wehave considered theoretically normal metal - FeBS (N-S�) junctions, FeBS breakjunctions and contacts between usual single-band s-wave superconductor andFeBS (S-S� junctions). We have demonstrated that investigation of current-voltagecharacteristics of N-S� junctions and FeBS break junctions provides the possibilityto distinguish possible ++ and +− symmetries of the order parameter in FeBS. Wealso have calculated phase dependencies of the Josephson current and tempera-ture dependencies of critical Josephson current across S-S� junctions for diferent

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directions of current relative to the crystallographic axes of FeBS and diferentlengths of an insulator layer. We have demonstrated, that the investigation ofcurrent-phase dependencies of S-S� Josephson junctions also allows to distinguishpossible symmetries of the order parameter in FeBS [3,4]. We have conirmed mi-croscopically the recently proposed experimental scheme to determine the sym-metry of the order parameter in FeBS [5], and suggest a new experimental schemebased on measurement of an amplitude of the second harmonic of phase depen-dence of the Josephson current in diferent directions relative to crystallographicaxes of FeBS.

The proposed approach [1,2] can be applied for microscopic calculations ofa normal and the Josephson current across junctions with other new uncon-ventional superconductors, such as Sr2RuO4, doped superconducting insulatorsCuxBi2Se3 because they are also multiorbital metals. Also we demonstrate theapplication of our approach to calculations of the proximity efect in contacts be-tween usual s-wave superconductor and 3D topological insulator, taking into ac-count its orbital degrees of freedom.

The work is supported by the RFBR, Grants № 13-02-0185, 14-02-31366-mol_a,15-52-50054 and by the Ministry of Education and Science of the Russian Federa-tion, Grant № 14Y26.31.0007.

References:1. A. V. Burmistrova, I. A. Devyatov, JETP Lett. 95, 239 (2012).2. A. V. Burmistrova, I. A. Devyatov, A.A. Golubov, K. Yada and Y. Tanaka, J.

Phys. Soc. Jpn. 82, 034716 (2013).3. A. V. Burmistrova, I. A. Devyatov, EPL (Europhysics Letters), 107, 67006,

(2014).4. A. V. Burmistrova, I. A. Devyatov, A. A. Golubov et. al, Phys. Rev. B, 214501,

(2015).5. A. A. Golubov and I. I. Mazin, Appl. Phys. Lett., 102, 032601 (2013).

Specular Interband Andreev Relections in GrapheneDmitri Efetov

Massachusets Institute of Technology, Cambridge, USA


Electrons incident from a normal metal onto a superconductor are relectedback as holes — a process called Andreev relection. In a normal metal wherethe Fermi energy is much larger than a typical superconducting gap, the relectedhole retraces the path taken by the incident electron. In graphene with ultra low

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disorder, however, the Fermi energy can be tuned to be smaller than the supercon-ducting gap. In this unusual limit, the holes are expected to be relected specularlyat the superconductor-graphene interface due to the onset of interband Andreevprocesses, where the efective mass of the relected holes change sign. Here wepresent measurements of gate modulated Andreev relections across the low dis-order van der Waals interface formed between graphene and the superconductingNbSe2. We ind that the conductance across the graphene-superconductor inter-face exhibits a characteristic suppression when the Fermi energy is tuned to val-ues smaller than the superconducting gap, a hallmark for the transition betweenintraband retro- and interband specular- Andreev relections.

Cascade of Phase Transitions Near Quantum Critical PointKonstantin Efetov

Ruhr University Bochum, Germany; National University of Science and TechnologyMISIS, Moscow, Russia


In the standard picture of a quantum phase transition, a single quantum crit-ical point separates the phases at zero temperature. Here we show that the two-dimensional case is considerably more complex. Instead of the single point sep-arating the antiferromagnet from the normal metal, we have discovered a broadregion between these two phases where the magnetic order is destroyed but com-pletely diferent phases arise. Depending on parameters characterizing the Fermisurface, one obtains a nematic state followed by a charge density wave (CDW),superconductivity and a broad region with strong luctuations where the CDWcompetes with supercondcutivity. Both the superconductivity and CDW havethe d-wave symmetry. In the situation when the transition temperature of thenematic state exceeds the transition temperatures into the other states, the mod-ulation vector of CDW is directed along the directions of the nematicity and isincommensurate with the spin modulation of the parent antiferromagnet. In themost important case of CuO lattice of high superconducting cuprates, this cor-responds to a charge modulation on the � atoms along the bonds. The strongcompetition between the superconductivity and CDW can destroy the long rangeorder of both the phases and this may explain the pseudogap state in the cuprates.At lower temperatures, the luctuations are less essential and superconductivitybecomes stable. Applying a magnetic ield destroys the superconductivity butstabilizes CDW.

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The results of our theory can serve as explanation of recent experiments oncuprates performed with the help of STM, NMR, hard and resonant soft X-rayscattering, sound propagation, and with some other techniques.

Time-Reversal Broken Chiral Superconducting Phase Driven byElectronic Correlations in TiSe2

Dmitry EfremovLeibniz Institute for Solid State and Materials Research, Dresden, Germany


TiSe2 is a quasi-two dimensional material which hosts CDW and supercon-ducting orders. Motivated by recent progress on single-layer transition metaldichalcogenides, we study the efects of electronic correlations in single-layerTiSe2. We use renormalization group (RG) analysis to ind low energy couplingsand possible long range orders. Our results suggest that TiSe2 shows competitionbetween charge density wave (CDW) order competes with two forms of super-conductivity, both unconventional. One possibility is s+- order analogous to thepnictides. The second is chiral superconductivity, with possible + symmetry.

Doping Asymmetry of Superconductivity Coexisting withAntiferromagnetism in Spin Fluctuation Theory

Ilya EreminRuhr-Universität Bochum, Institut für Theoretische Physik, Bochum, Germany


We generalize the theory of Cooper-pairing by spin excitations in the metal-lic antiferromagnetic state to include situations with electron and/or hole pock-ets. We show that Cooper-pairing arises from transverse spin waves and fromgapped longitudinal spin luctuations of comparable strength. However, eachof these interactions, projected on a particular symmetry of the superconductinggap, acts primarily within one type of pocket. We ind a nodeless �− � -wavestate is supported primarily by the longitudinal luctuations on the electron pock-ets, and both transverse and longitudinal luctuations support nodal �− � -wave

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symmetry on the hole pockets. Our results may be relevant to the asymmetry ofthe AF/SC coexistence state in the cuprate phase diagram.

Strongly Correlated Electrons in High TemperatureSuperconductors

Alvaro FerrazInternational Institute of Physics-UFRN, Brazil


We present an overview of the ield- theoretical renormalization group ap-proach for the normal phase of the optimally doped cuprates. Earlier calculationspredicted sucessfully the existence of d-wave charge instabilities (d-CDW) whichwere later veriied in several experiments in non-Lanthanum-based compounds.However the reasons for the onset of the so-called pseudogap phase remains anopen problem. We discuss possible solutions for this riddle.

Escape and Retrapping in Josephson � JunctionsEdward Goldobin1, M. Weides2, R. Mendito1, B. Neumeier1, D. Koelle1, R.

Kleiner11: Physikalische Institut, Experimentalphysik II, University of Tübingen, Germany

2: Karlsruhe Institute of Technology, Karlsruhe, Germany


Recently, our group has demonstrated experimentally [1] the irst� Josephsonjunction (JJ) based on a superconducting-insulator-ferromagnet-superconductor(SIFS) heterostructure with tailored F-layer. Such a � JJ has very unusual prop-erties [2], e.g., a �� periodic double-well energy proile, which leads to a dou-bly degenerate ground state with the phases −� and +�, two critical currents ±and non-trivial retrapping dynamics expected [3]. The irst potential applicationswere demonstrated, e.g., a memory cell [4]. In this talk I will describe our recentexperiments with ±� JJs.

First, we investigated the retrapping of the phase in SIFS � JJs [5]. By mea-suring the switching current histograms, we able to calculate the probability ofthe phase to be trapped in −� and +� wells when the junction returns from non-zero- to zero-voltage-state. We show that, similar to the theoretical prediction [3],

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at high temperature the retrapping is deterministic (always in the +�well), whileat lower temperature we observe an onset of the butterly efect with an oscillat-ing probability of trapping in a particular well. Unexpectedly, the probability oftrapping in a particular well saturates at a value diferent than 50% at low tem-peratures.

Second, we investigated the escape of the phase in artiicial � JJs, made us-ing conventional Nb–AlOx –Nb JJ equipped with tiny current injectors to create aphase discontinuity � ∼ �. We have measured the switching current histogramsin a wide temperature range from 1K down to 20mK. Each histogram, in general,exhibits two escape peaks corresponding to critical currents ±, having the width�±. The dependences �±( ) stop decreasing below some temperature, which is in-terpreted as macroscopic quantum tunneling (MQT) of the phase. To our knowl-edge, this is the irst experimental observation of MQT in � JJ.

References:1. H. Sickinger, A. Lipman, M. Weides, R. G. Mints, H. Kohlstedt, D. Koelle, R.

Kleiner, E. Goldobin, “Experimental evidence of a � Josephson junction”,Phys. Rev. Lett. 109, 107002 (2012). DOI:10.1103/PhysRevLett.109.107002

2. E. Goldobin, D. Koelle, R. Kleiner and A. Buzdin, “Josephson junctions withsecond harmonic in the current-phase relation: properties of � junctions”,Phys. Rev. B 76, 224523 (2007). DOI:10.1103/PhysRevB.76.224523

3. E. Goldobin, R. Kleiner, D. Koelle, R.G. Mints, “Phase Retrapping in a Point-like � Josephson Junction: The Buttery Efect”, Phys. Rev. Lett. 111, 057004(2013). DOI:10.1103/PhysRevLett.111.057004

4. E. Goldobin, H. Sickinger, M. Weides, N. Ruppelt, H. Kohlstedt, R. Kleiner,and D. Koelle, “Memory cell based on a � Josephson junction”, Appl. Phys.Lett. 102, 242602 (2013). DOI:10.1063/1.4811752

5. submitted to Phys. Rev. Lett. (June 2015)

Novel Nb/Pd0.99Fe0.01/Nb Josephson Junction Magnetic Switchesfor Cryogenic Memory

Igor Golovchanskiya,b, Vitaly V. Bolginova,c, Nikolay N. Abramova, Valery V.Ryasanova,c

a: National University of Science and Technology MISIS, Moscow, Russiab: Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia

c: Institute of Solid State Physics, Russian Academy of Science, Chernogolovka, MoscowRegion, Russia


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A novel Josephson magnetic memory element based on Josephson supercon-ductor/ferromagnet/superconductor tunnel junction (SFS junction) is presented.Josephson barrier is a Pd0.99Fe0.01 ferromagnetic layer with in-plane magneticanisotropy and small coercive ield. An application of small external magneticield changes the magnetization of ferromagnetic layer that in turn changes thejunction critical current , allowing the realization of two distinct states with highand low corresponding to logical “0” and logical “1” states respectively [1-3].Dynamical properties (i.e. gyromagnetic ratio, Gilbert damping constant, etc.) ofPd0.99Fe0.01 ferromagnetic layer are investigated separately employing high sensi-tive ferromagnetic resonance experiment. A re-magnetization (switching) processof Pd0.99Fe0.01 layer is studied numerically and limiting magnetization switchingrate is derived.

References:1. V.V. Bol’ginov, V.S. Stolyarov, D.S. Sobanin, A.L. Karpovich, and V.V.

Ryazanov, JETP Lett. 95, 366 (2012).2. Valery V. Ryazanov, Vitaly V. Bol’ginov, Danila S. Sobanin, Igor V. Vernik,

Sergey K. Tolpygo, Alan M. Kadin, and Oleg A. Mukhanov, Physics Procedia36, 35 (2012).

3. I.V. Vernik, V.V. Bol’ginov, S.V. Bakurskiy, A.A. Golubov, M.Yu. Kupriyanov,V.V. Ryazanov, and O.A. Mukhanov, IEEE Trans. Appl. Supercond. 23,1701208 (2013).

Spectroscopy of Surface Andreev Bound States in TopologicalInsulator / Superconductor Junctions

Alexander Golubov1,2, M. Snelder1, Y. Asano2,3, M Stehno1, and A. Brinkman11: Faculty of Science and Technology and MESA; Institute of Nanotechnology, University

of Twente, Netherlands2: MIPT, Dolgoprudny, Russia

3: Hokkaido University, Sapporo, Japan


The results of recent studies of superconducting junctions on surfaces of topo-logical insulators are presented. To guide experimental work on the search forMajorana zero-energy modes, we calculate the superconducting pairing symme-try of a three-dimensional topological insulator in combination with an s-wavesuperconductor. In analogy to the case of nanowires with strong spin-orbit cou-pling we show how the pairing symmetry changes across diferent topologicalregimes. We demonstrate that a dominant p-wave pairing relation is not sui-cient to realize a Majorana zero-energy mode useful for quantum computation.

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The relation between odd-frequency pairing and Majorana zero energy modesis derived by using Green functions techniques in three-dimensional topologicalinsulators in the so-called Majorana regime. We discuss thereafter how the pair-ing relations in the diferent regimes can be observed in the shape of the tunnel-ing conductance of an s-wave proximized three-dimensional topological insula-tor. We discuss the necessity to incorporate a ferromagnetic insulator to localizethe zero-energy bound state to the interface as a Majorana mode. We also presentthe results of conductance spectroscopy measurements of a proximity inducedsuperconducting topological insulator. We study the proximity efect betweenthe fully-gapped region of a topological insulator in direct contact with an s-wavesuperconducting electrode (STI) and the surrounding topological insulator lake(TI) in Au/Bi1.5Sb0.5Te1.7Se1.3/Nb devices. The conductance spectra of the devicesshow the presence of a large induced gap in the STI as well as the induction of su-perconducting correlations in the normal part of the TI on the order of the Thou-less energy. The shape of the conductance modulation around zero-energy variesbetween devices and can be explained by existing theory of s-wave-induced su-perconductivity in SNN’ (S is a superconductor, N a superconducting proximizedmaterial and N’ is a normal metal) devices.

Anomalous Proximity Efect and More Than One MajoranaFermion

Satoshi Ikegaya, Y. AsanoDepartment of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan


Physics of Majorana fermion has been a hot issue in condensed matterphysics.Within this context, the anomalous proximity efect of spin-triplet su-perconductorshas been growing its importance because the efect is a direct re-sult of the existence of Majorana fermion bound states.An isolating spin-triplet� -wave superconductor, for instance, traps highly degenerated Majorana boundstates at its edges. When we attach the normal metal to the � -wave supercon-ductor, the Majorana bound states penetrate into the normal metal and enhancethe local density of states at the zero energy [1]. The penetrated Majorana boundstates induce various anomalous electromagnetic properties in the normal metal.For example, a perfect Andreev relection from a � -wave superconductor into adirty normal metal causes anomalous low energy transport in the -direction suchas a zero-bias conductance quantization in normal-metal/superconductor (NS)junctions [2]. The perfect quantization of the zero-bias conductance in the disor-

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dered junction is an aspect of the anomalous proximity efect. The zero-bias con-ductance quantization implies that the penetrated Majorana fermions retain theirhigh degeneracy even in the impurity potentials and form the resonant transmis-sion channels there. However, it has been unclear what symmetry protects thedegeneracy of Majorana fermions in the dirty normal metal and why the perfectAndreev relection persists at zero-energy.

Recent theoretical studies have shown that chiral symmetry is responsible forthe stability of more than one Majorana fermion [3]. On the basis of the novel in-sight, we successfully explain the stability of the degenerated Majorana fermionsin the disordered normal metal and prove the perfect Andreev relection irrespec-tive of impurity potentials [4]. In our poster, we explain how chiral symmetryprotect the degeneracy and how chiral nature of � -wave superconductor inducethe perfect Andreev relection.

References:1. Y. Tanaka, Y. Asano, A. A. Golubov, and S. Kashiwaya, Phys. Rev. B 72,

140503(R) (2005).2. Y. Tanaka and S. Kashiwaya, Phys. Rev. B 70, 012507 (2004).3. S. Tewari and J. D. Sau, Phys. Rev. Lett. 109, 150408 (2012).4. S. Ikegaya, Y. Asano, and Y. Tanaka, Phys. Rev. B 91, 174511(2015).

High- and Low Superconductivity and Superluidity inFermi-Systems with Repulsion

Maxim KaganP.L. Kapitza Institute for Physical Problems, RAS, Moscow


Recent discovery of Cooper pairing at 190 K in metallic hydrogen sulide un-der pressure revives the hopes to proceed from high- to room superconduc-tivity. In the same time there are many interesting low- superconductive andsuperluid systems.

In the present talk we discuss high- and low superconductivity and su-perluidity in 3D and 2D fermionic systems with purely repulsive interaction. Weconstruct the phase-diagrams and ind the regions of superconductive pairings infree space and on diferent lattices in Hubbard, t-J and other models of stronglycorrelated electron systems. We demonstrate the possibility to increase signii-cantly already at low density of fermions in the spin-polarized case and in the two-band situation. The proposed theory can explain or predict superconductivity indiferent materials including high- superconductors, low heterostructures

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and semimetals, heavy fermions and organic superconductors. It explains angu-lar dependence of the superconductive gap in FeAs-based superconductors andpredictis Kohn-Luttinger superconductivity in idealized monolayer and bilayergraphene. For physics of quantum liquids and gases the theory predicts tripletp-wave superluidity in 3D and 2D mixtures of He-3 in He-4 and in ultracoldFermi-gases in magnetic traps, as well as a strong increase in spin-polarisedA1-phase of the superluid He-3. The potential for the experimental realization of“high- ” superluidity in spin-polarized (imbalanced) Fermi-gases has the groupof J.E.Thomas in North Carolina. The physics of Dirac points in graphene has im-portant analogies with the 2D honeycomb optical lattices studied by T.Esslingerteam in Zurich.

Dielectric Susceptibility of Magnetoelectric Thin Films withVortex-Antivortex Dipole Pairs

Petr Karpov, Sergei MukhinDepartment of Theoretical Physics and Quantum Technologies, National University of

Science and Technology MISiS, Leninski avenue 4, 119049, Moscow, Russia


In the present work [1] we consider a model for magnetoelectric or type-II mul-tiferroic [2] thin ilms and ind the inluence of metastable micromagnetic struc-tures (vortex-antivortex pairs) on electric properties (dielectric susceptibility) ofthe system.

We describe the magnetic subsystem using continuous version of the 2D XYmodel (XY plane coincides with the ilm plane). It is well known [3,4] that insuch systems vortices play an important role: below � (Berezinskii-Kosterlitz-Thouless temperature) vortices and antivortices are bound in pairs and when thetemperature rises above � the pairs dissociate.

If we now include the interaction between the electric and magnetic subsys-tems in form of [5] � −��((�∇)� −�(∇�))( is the interaction energy density, � is the polarization, � is the magnetiza-tion, � is the coupling constant), then magnetic vortices acquire electric charges.In the work we calculate the contribution of the vortex dipole pairs to the dielectricsusceptibility of the system at � � .

In order to do this, we write the grand partition function for the vortex-antivortex dipole gas in the external electric ield. It turns out that it is possibleto calculate the grand partition function in the approximation of noninteracting

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dipole pairs and to obtain the contribution of the pairs to the electric susceptibil-ity �( ) (which is the main result of the paper). As → � the susceptibility takesan activation exponential form �( )( ) ∼ exp(−� � ) (� is the vortex-antivortexcreation energy) and as → � it diverges as �( )( ) ∼ | − � |− . However,we expect that in the vicinity of � the interaction of dipole pairs becomes im-portant and, therefore, at � susceptibility stays inite. Nevertheless one shouldobserve a sharp peak in �( )( ) dependence at ≈ � in the experimental data.

References:1. P.I. Karpov, S.I. Mukhin. Dielectric susceptibility of magnetoelectric thin ilms with

vortex-antivortex dipole pairs. arXiv:1506.07856 (2015).2. D.I. Khomskii. Classifying multiferroics: Mechanisms and efects. Physics 2, 20

(2009).3. J.M. Kosterlitz and D.J. Thouless. Ordering, metastability and phase transitions

in two-dimensional systems. J.Phys. C6, 1181 (1973).4. V.L. Berezinskii. Destruction of long-range order in one-dimensional and two-

dimensional systems having a continuous symmetry group I. Classical systems.Sov.Phys. JETP 32, 493 (1971).

5. M.V. Mostovoy. Ferroelectricity in spiral magnets. Phys.Rev.Lett. 96, 067601(2006).

Current Transport in SF-NFS Josephson Structures: Theory andApplication

I. I. Soloviev1,2, Nikolay Klenov3,2, S. V. Bakurskiy3,4,5, V. V. Bol’ginov6,7, V. V.Ryazanov6,7, M. Yu. Kupriyanov1,4, and A. A. Golubov4,5

1: SINP, MSU, Moscow, Russia2: NIIFP, Zelenograd, Russia

3: Physics Department, MSU, Russia4: MIPT, Dolgoprudniy, Russia

5: University of Twente, The Netherlands6: ISSP, Chernogolovka, Russia

7: NUST MISiS, Moscow, Russia


We propose a control element for a Josephson spin valve. It is a complexJosephson device containing ferromagnetic (F) layer in the weak-link area consist-ing of two regions, representing 0 and p Josephson junctions, respectively. Thevalve’s state is deined by mutual orientations of the F-layer magnetization vectorand boundary line between 0 and p sections of the device. We consider possi-ble implementation of the control element by introduction of a thin normal metal

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layer in a part of the device area. By means of theoretical simulations, we studyproperties of the valve’s structure as well as its operation, revealing such advan-tages as simplicity of control, high characteristic frequency, and good legibility ofthe basic states.

In addition we discuss several general properties of the current transportthrough a long Josephson junction with alternating critical current density. Thisalternating density can be achieved in experiment by incorporating of the mag-netic layer to the weak link in a special way. Prospects for the practical use of suchstructures are related to the possibility of obtaining bistable Josephson elementson their basis. Joint analysis for both the current-phase relations and the dynamiccharacteristics allowed to optimize the operation mode for fast superconductingmemory cell based on the bistable contact and to assess the energy dissipation for”Read” and ”Write” operations.

Controllable Tuning of Spin-Singlet and Spin-Triplet Currents in aJosephson Spin-Valve

A. Iovan, T. Golod, and Vladimir KrasnovStockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden


It has been predicted theoretically [1,2] that the proximity efect in a supercon-ducting spin-valve should strongly depend on a relative orientation of magnetiza-tion in ferromagnetic layers of the spin valve. An exotic spin-triplet component ofthe superconducting order parameter can be generated in the non-collinear stateof the superconducting spin-valve. Several experimental reports, conirming sucha behavior, has been made [3-5]. However, unambiguous interpretation of thedata requires accurate control of the spin-valve state. This also presumes a mono-domain state of the spin-valve, which requires special care.

In this talk we present our recent results on experimental analysis of nano-scale superconducting spin-valve devices, in which a spin valve structure is imple-mented as a barrier in a Josephson junction. Nano-scale junctions with sizes downto 150 nm were patterned by photolithography, reactive ion etching and three-dimensional nano-sculpturing using focused ion beam, as described in Ref. [6].Small dimensions were necessary both for mono-domain switching of spin valvesand for enhancement of junction resistances to comfortably measurable values.Ferromagnetic layers in the spin-valve are made dissimilar using a combination ofdiluted (CuNi) ferromagnets with diferent Ni concentration of with combinationof diferent strong (Ni, Co, Py) ferromagnets. Our Josephson spin-valves exhibit

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both clear Fraunhofer-type modulation of the Josephson critical current ( ), in-dicating good homogeneity of the Josephson current through the spin valve, anda regular spin-valve magnetoresistance with minima at the parallel and maximaat the anti-parallel orientation of magnetization of the two ferromagnetic layers[7].

We put special eforts to development of accurate ways for in-situ analysis ofthe spin-valve state. We demonstrate how two-dimensional angular orientationof magnetic moments of ferromagnetic layers in the spin-valve can be accuratelymeasured in-situ. This allows us to make an unambiguous connection betweenthe relative orientation of magnetizations and the amplitude of the Josephson cur-rent, which indicate that both the spin-singlet and the spin-triplet components ofthe supercurrent are tuned with changing the orientation of the spin-valve.

References:1. A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).2. F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys. 1321 (2005).3. C. Bell, G. Burnell, C. W. Leung, E. J. Tarte, D.-J. Kang, and M. G. Blamire,

Appl. Phys. Lett. 84, 1153 (2004).4. T. S.Khaire, M. A. Khasawneh, W. P. Pratt, Jr., and N. O. Birge, Phys. Rev.

Lett. 104, 137002 (2010).5. P. V. Leksin, N. N. Garif’yanov, I. A. Garifullin, J. Schumann, V. Kataev, O.

G. Schmidt, and B. Buchner, Phys. Rev. Lett. 106, 067005 (2011).6. T. Golod, A. Rydh, and V.M. Krasnov, Phys. Rev. Lett., 104, 227003 (2010).7. A. Iovan, T. Golod, and V.M. Krasnov, Phys. Rev. B, 90, 134514 (2014).

Josephson Efect in SIFS Tunnel Junctions with ComplexBarriers in Weak Link Region

S.V. Bakurskiy+∗, A.A.Baranov∗, A.A.Golubov∗×, N.V.Klenov+, MikhailKupriyanov∗◦, I. I. Soloviev◦

+: Physics Department, Lomonosov MSU, 119991 Moscow, Russia∗: Moscow Institute of Physics and Technology, 141700 Dolgoprudniy, Russia

×: Faculty of Science and Technology and MESA+, Institute for Nanotechnology,University of Twente, 7522 NB Enschede, Netherlands

◦: Skobeltsyn Institute of Nuclear Physics, Lomonosov MSU, 119991 Moscow, Russia: Institute of Physics, Kazan (Volga region) Federal University, 420008 Kazan, Russia


We study theoretically the properties of SIFS type Josephson junctions com-posed of two superconducting (S) electrodes separated by an insulating layer (I)and a ferromagnetic (F) region consisting of periodic magnetic domains structure

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with antiparallel magnetization directions in neighboring domains. Two domainalignments have been considered. In the irst geometry it is supposed that thedomain structure is formed in a single ferromagnetic ilm. It is a periodical struc-ture in the direction perpendicular to the current lowing through the junction.In the second geometry it is considered that the Josephson coupling occurs inSFNFN…FNIS structures, in which in weak link there is a FNFN…FN multilayerwith FN interfaces located perpendicular to the direction of supercurrent low.

For the irst geometry the two-dimensional problem in the weak link area issolved analytically in the framework of the linearized quasiclassical Usadel equa-tions. Based on this solution, the spatial distributions of the critical current den-sity, Jc, in the domains and critical current, Ic of SIFS structures are calculated asa function of domain wall parameters, as well as the thickness, dF and the width,W, of the domains. We demonstrate that Ic(dF,W) dependencies exhibit dampedoscillations with the ratio of the decay length, xi1, and oscillation period, xi2, be-ing a function of the parameters of the domains, and this ratio may take any valuefrom zero to unity. Thus, we propose a new physical mechanism that may explainthe essential diference between xi1 and xi2 observed experimentally in varioustypes of SFS Josephson junctions.

In the second geometry we study the proximity efect in SFNFN…FN elec-trode in the frame of Usadel equations both analytically (in the linear approxi-mation) and numerically. We have shown that depending on the layers thicknessand magnitude of suppression parameters gamma and gammaB superconductingcorrelations can monotonically decay in FNFN..FN multilayer or exhibit dampedoscillations and calculate the decay length, xi1, and oscillation period, xi2, as afunction of layers thickness and suppression parameters at FN boundaries.

This work was supported by RFBR grants l4-02-90018-bel a, 14-02-31002-mola, 15-32-20362-mol a ved, Ministry of Education and Science of the Russian Fed-eration in the framework of Grant No. 14Y26.31.0007 and the Program for thePromotion of Competitiveness of the Kazan Federal University among the World-Leading Scientiic Educational Centers, Russian President grant MK-1841.2014.2,Dynasty Foundation, Scholarship of the President of the Russian Federation andDutch FOM.

SnS-Andreev Spectroscopy of Fe-based Oxypnictides: Scaling ofSuperconducting Parameters with �

Tatiana Kuzmicheva1,2, S.A. Kuzmichev2, Ya.G. Ponomarev2, V.M. Pudalov11: P.N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia

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2: M.V. Lomonosov Moscow State University, 119991 Moscow, Russia


We studied high-temperature oxypnictide (so called 1111 family) Fe-basedsuperconductors LaO1–xFxFeAs, GdO1–xFFeAs, GdO1–δFeAs, Sm1–xThxOFeAsand CeO1–xFxFeAs with the � range �� − �� K by Andreev and intrinsic An-dreev spectroscopies [1,2]. Intrinsic multiple Andreev relections efect was irstlyobserved in 1111-oxypnictides, revealing the Andreev-like transport along the c-direction. We determined the values of two bulk superconducting gaps and theirBCS-ratios, and demonstrated weak anisotropy of Δ (�� − ��%) and the absenceof nodes in Δ . For the maximal � ≈ �� K, we found Δ � �� ± �� meV,Δ � �� ± �� meV, Δ �Δ ≈ ��.

The gap temperature dependences Δ � ( ) agree well with two-band modelby Moskalenko and Suhl [3]. Both gaps turn to zero at common critical tempera-ture. Using itting of the experimental Δ � ( ) by the two-band model, we deter-mined some parameters of superconducting state of 1111-materials directly fromthe experiment.

The estimated relative coupling constants � were shown to be� �� |� |�|� | ≈ �� within the range � � �� − �� K. Wedemonstrate scaling of both superconducting gaps with � (Fig. 1) and nearlyconstant BCS-ratio �Δ � � � ≈ ��. For each condensate, the eigen BCS-ratiowas estimated (in a hypothetical case of zero interband coupling, � , � � �):for the large gap we get �Δ � � � ≈ ��, for the small gap �Δ � � � ≈ ��,�� ≈ ��8. These values exceed the weak-coupling limit but are in frames ofEliashberg theory thus pointing to a strong electron-phonon intraband couplingin two condensates. The lanthanide-� spacers were shown to act as chargereservoirs.

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Fig 1: The dependence of the large superconducting gap (solid symbols) andthe small gap (open symbols) on the critical temperature for oxypnictides andFeSe. The weak-coupling BCS-limit is shown by dash-dot line for comparison.

References:1. T.E. Kuzmicheva, et al., EPL 102, 67006 (2013)2. T.E. Kuzmicheva, et al., Physics-Uspekhi 57, 819 (2014)3. V.A. Moskalenko, Fiz. Met. Metall. 8, 503 (1959); H. Suhl, et al., Phys. Rev.

Lett. 3, 552 (1959)

Paramagnon Excitations Theory for Magnetic Properties ofLayered Copper Oxide Superconductors

Igor LarionovNational University of Science & Technology ”MISIS”, 119049, Moscow, Russia

Kazan Federal University, 420008, Kremlevskaya, 18, Kazan, Russia


Using a relaxation function theory we obtain and analyze the dynamic spinsusceptibility expressions for doped � �� two-dimensional Heisenberg antifer-romagnetic (AF) model in the paramagnetic phase taking into account the thermaldamping efects of spin wave-like (paramagnon-like) excitations. The relaxation

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function theory is widely applicable for describing the properties of nonequilib-rium systems and by itself the Markovian situation can be valid even in the ab-sence of any picture of the system in terms of well-deined excitations [1]. Thepresentation is valid for all wave vectors throughout the Brillouin zone.

The role of damping (lifetime) of paramagnon excitations, its evolution withdoping and temperature, is highlighted in view of magnetic response of high-

layered cuprates. It is shown [2] that the theory is able to explain the mainexperimentally observed features in the imaginary part of the dynamic spin sus-ceptibility in La2–xSrxCuO4 and YBa2Cu3O7–δ as obtained by resonant inelasticX-ray scattering (RIXS) [3]. The calculated dynamic spin susceptibility [4] givesalso a reasonable agreement with neutron scattering experiments [5] and nuclearspin-lattice relaxation rates �� [6] data from pure AF insulator right up to opti-mally doped high- ’s in the normal phase. It is shown that RIXS data analysisdepends on paramagnon damping and thus afected by approximations made forexpressions for dynamic spin susceptibility.

References:1. U. Balucani, M. H. Lee, and V. Tognetti, Phys. Rep. 373, 409 (2003).2. I.A. Larionov, Solid State Commun. 208, 29 (2015) and to be published.3. M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M. Moretti Sala, V. Hinkov, M.

W. Haverkort, M. Minola, M. Bakr, K. J. Zhou, S. Blanco-Canosa, C. Monney,Y. T. Song, G. L. Sun, C. T. Lin, G. M. De Luca, M. Salluzzo, G. Khaliullin, T.Schmitt, L. Braicovich, B. Keimer, Nature Physics Vol. 7, 725-731 (2011).

4. I.A. Larionov, Phys. Rev. B 69, 214525 (2004); 72, 094505 (2005); 76, 224503(2007)

5. B. Keimer, N. Belk, R. J. Birgeneau, A. Cassanho, C. Y. Chen, M. Greven, M.A. Kastner, A. Aharony, Y. Endoh, R. W. Erwin, and G. Shirane, Phys. Rev.B 46, 14034 (1992).

6. T. Imai, C. P. Slichter, K. Yoshimura, and K. Kosuge, Phys. Rev. Lett. 70,1002 (1993).

Josephson Junction Detectors for Majorana and Dirac FermionsMoitri Maiti1, K. M. Kulikov1, K. Sengupta2, and Y. M. Shukrinov1

1: BLTP, JINR, Dubna, Russia2: Indian Association for the Cultivation of Science, Kolkata, India


We demonstrate that the current—voltage (I—V) characteristics of resistivelyand capacitiver shunted Josephson junctions (RCSJ) of topological superconduc-tors hosting localized subgap Majorana states provides a phase sensitive method

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for their detection. We show that the I—V characteristics of such RC—SJ s displaya novel devil staircase structure for Shapiro steps which is qualitatively difer-ent from those found in conventional superconductors. A similar study for RCSJwith graphene superconducting junctions hosting Dirac—like quasiparticles re-veals that the Shapiro step width in their I—V curves oscillates with the junctionbarrier potential. We demonstrate that this oscillatory feature is a signature of theunderlying Dirac quasiparticles.

Three Component Spin-Charge Superconducting OrderParameter and Pair Density Waves in Correlated Fermi Systems

in a Magnetic FieldSergei Matveenko

Landau Institute for Theoretical Physics, Moscow


A irst-order phase transition is predicted between a spatially homogeneoussuperconducting state and a state with a space-modulated composite spin-charge-superconducting order parameter in an applied external magnetic ield. In thisstate the superconducting order changes sign when entering the “stripe-phase”ordered domain. Corresponding self-consistent solutions of the Bogoliubov-deGennes equations are found in an analytic form for the two-dimensional Hubbardt-U-V model with �− � symmetry of the superconducting order parameter in anexternal magnetic ield.

Microscopic Theory of Vortex Pinning on Columnar Defects inConventional, Chiral and Ferromagnetic Superconductors

Alexander Mel’nikov1,2, A.V.Samokhvalov1, and V.Vadimov1,21: Institute for Physics of Microstructures, RAS, Nizhny Novgorod, Russia

2: Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia


The electronic structure of a vortices pinned by an insulating columnar in-clusions in type-II superconductors is studied within the Bogolubov-de Gennestheory. For conventional s-wave superconductors we ind the modiication of theanomalous spectral branch in the quasiparticle spectrum caused by the electronscattering at the defect. For a chiral px+i py superconductor the structure of the

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anomalous spectral branch is shown to be strongly afected by the mutual orienta-tions of the angular momenta of the center of mass and the relative motion of thetwo electrons in the Cooper pair. Being only slightly perturbed by the scatteringat the defect for the zero sum of these angular momenta the anomalous spectralbranch appears to change dramatically in the absence of such compensation. Inthe latter case the defect presence changes the anomalous branch slope sign atthe Fermi level resulting in the quasiparticle angular momenta inversion at thepositive energies and the impact parameters smaller than the defect radius. Weanalyze also the pinning and electronic structure of multiquanta vortices.

The experimentally observable consequences for the scanning tunneling mi-croscopy characteristics and high-frequency ield response (in particular, Kerr ef-fect) are discussed. The individual pinning potentials and corresponding depin-ning currents are evaluated. The chiral superconductors are shown to reveal astrong dependence of the pinning characteristics on the mutual orientation of themagnetic ield and internal angular momentum of the Cooper pair. The pinningphenomena in chiral are also shown to be strongly afected by the quasiparticleedge currents lowing around the insulating defects. The resulting contributionto the pinning potential is found to be similar to the one for pinned vortices inferromagnetic superconductors.

Triplet Proximity Efect in Superconducting Heterostructures witha Half-Metallic Layer

Sergey Mironov1,2,3 and A. Buzdin11: University Bordeaux, Talence Cedex, France

2: MIPT, Dolgoprudny, Russia3: Institute for Physics of Microstructures RAS, Nizhny Novgorod, Russia


We present the Usadel theory describing the superconducting proximity ef-fect in heterostructures with a half-metallic layer. It is shown that the full spin po-larization inside the half-metals gives rise to the giant triplet spin-valve efect insuperconductor (S) – ferromagnet (F) – half-metal (HM) trilayers as well as to thephi-junction formation in the S/F/HM/F/S systems. In addition, we consider theexactly solvable model of the S/F/HM trilayers of atomic thickness and demon-strate that it reproduces the main features of the spin-valve efect found within theUsadel approach. Our results are shown to be in a qualitative agreement with therecent experimental data on the spin-valve efect in MoGe/Cu/Ni/CrO2 hybrids[A. Singh et al., arXiv:1410.4973].

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Interference of Triplet -wave Condensates in CoupledJosephson Junctions

Andreas Moor1, A.F. Volkov1, K.B. Efetov1,21: Ruhr-Universität Bochum, Germany

2: NUST “MISiS”, Moscow, Russia


Interest in studying triplet superconducting correlations in superconduc-tor/ferromagnet (S/F) hybrids has substantially increased during the past decade(see reviews and references therein [1,2]). In this talk we present results of thetheoretical study of dc Josephson efect in a multiterminal structure of cross-typegeometry in which the Josephson coupling between is realized through the long-range triplet component (LRTC). The triplet Cooper pairs are created in S/F(S �S/F ) bilayers with a good interface which consist of a standard singlet BCSsuperconductors S and a weak ferromagnet with an exchange ield �. The singletcomponent is separated by spin ilters Fl (magnetic insulator) or by a strong fer-romagnet F . We show that the LRTCs interfere if the magnetic moments in spinilters are oriented in the same direction. If the vectors � are parallel, the Joseph-son current in the considered system S /Fl - n - S /Fl has the standard phasedependence � − sin�, but the critical current is negative (�-junction), wheren is a normal wire. In case of perpendicular �, the current is not zero at � � �(� - contact). In other words a spontaneous current may appear in the system.Interestingly, although the ilters, for example, pass only electrons with spin up,in the n-wire exist triplet Cooper pairs with both spin up and down. The resultsfor a system in which the ilters are replaced by a strong ferromagnet difer fromthose obtained for the system with ilters.

References:1. F. S. Bergeret, A. F. Volkov, K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005).2. M. Eschrig, Physics Today, 64, 43 (2011).

Geometrically Controlled Quantum Coherence andNon-Equilibrium Efects in Nanoscopic Kondo Droplets

Dirk MorrUniversity of Illinois at Chicago, USA


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The nature of strong correlations and quantum coherence in macroscopicKondo lattices, as realized in heavy fermion materials, still eludes theoretical un-derstanding. Atomic manipulation to assemble nanoscopic lattices of magneticatoms on metals – Kondo droplets – provides a new approach to study and con-trol the emergence of quantum coherence and interaction efects at the nanoscale,and thus bridge the gap between the single Kondo impurity and the ininite lat-tice. In this talk, I review some recent progress in controlling quantum coherenceand interactions in atomically precise periodic arrangements of magnetic atomson metallic surfaces using scanning tunneling microscopy (STM). I show howquantum-coherent coupling between individual Kondo resonances can be geo-metrically controlled, leading to local Kondo temperatures that are signiicantlyenhanced over that of a single magnetic atom. Moreover, I demonstrate how thenon-equilibrium transport properties of Kondo droplets provide new insight intothe nature of strong correlations.

Fluctuations of “Hidden Order” as Cooper Pairing GlueSergei Mukhin

Moscow Institute for Steel and Alloys, Moscow, Russia


Fluctuations of the “hidden order” as an origin of the Cooper pairing gluein high- superconductors is discussed. New scenario is based on the recentpublications [1]-[3] that introduced Euclidean crystallization in correlated fermi-system as an origin of a “hidden order”, that breaks translational invariance ofthe system along the Matsubara time exis. Spin-density wave with Matsubaratime-periodic amplitude is considered as a particular case of the “hidden order”.Fluctuations of this peculiar order parameter are found self-consistently and theirrole in providing a Cooper pairing glue in the fermi-system is investigated. Thework advances the previuos results. Namely, it was proven analytically [1] thatself-consistent Matsubara time-periodoc order parameter, built of Jacobian ellip-tic function, has zero scattering cross section and, therefore, is a candidate for a“hidden order”, emerging in the fermi-systems like high- cuprates. Simulta-neously, it is proven now analytically that this order parameter itself is only ametastable state of the fermi-system. The discrete spectrum of the “hidden or-der” luctuations is found using Lame functions theory. The new result consistsin the derivation, that shows how luctuations of the “hidden order”, forming adiscrete spectrum [2], [3], renormalize under the Cooper pairing in fermionic sys-tem. The self-consistent solution minimizing the efective Euclidean action of thefermi-system in a form of Landau-Ginzburg-Wilson functional with two coupled

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orders is found analytically as the major outcome of the work. Possible relation ofthe theory to the physics of high- cuprates is discussed.

References:1. S. I. Mukhin, «Spontaneously broken Matsubara’s time invariance in

fermionic system: macroscopic quantum ordered state of matter», J. Super-cond. Nov. Magn., vol. 24, 1165-1171 (2011).

2. S. I. Mukhin , «Euclidean action of fermi-system with ”hidden order”, Phys-ica B: Physics of Condensed Matter,v. 460, 264 (2015).

3. S. I. Mukhin, «Euclidian Crystals in Many-Body Systems: Breakdown ofGoldstone’s Theorem», J. Supercond. Nov. Magn.,vol.27, 945-950 (2014).

Charge Imbalance in a Stack of Intrinsic Josephson JunctionsUnder External Radiation

Yury Shukrinov1,2, Majed Nashaat3, Kulikov Kulikov1,2, Radwa Dawood3,Hussein El Samman4 and Th. M. El Sherbini3

1: BLTP, Joint Institute for Nuclear Research, Dubna, Russia2: Dubna International University of Nature, Society, and Man, Dubna, Russia

3: Department of Physics, Faculty of Science, Cairo University, Egypt4: Department of Physics, Faculty of Science, Menouiya University, Egypt


The nonequilibrium efects play an important role in a stack of intrinsic Joseph-son junctions (IJJs) in high temperature superconductors because the thickness ofthe superconducting layers is very small. Such efects can be manifested in a shiftof the condensate chemical potential and charge imbalance efect, where an elec-tron and a hole like quasi-particle distributions are diferent.

We investigate the efects of the non-stationary nonequilibrium charge imbal-ance on the phase dynamics for a stack of IJJs with diferent boundary condi-tions. The current-voltage characteristics of capacitively coupled Josephson junc-tions with the charge imbalance are numerically calculated and a precise numer-ical study is performed for a stack of IJJs under radiation. The efect of chargeimbalance is observed on the Shapiro step that shows a inite slope depending onthe nonequilibrium parameter, which is a function of the quasi-particle relaxationtime and the thickness of the superconducting layer. We demonstrate the shift ofthe Shapiro step from its canonical position determined by the frequency of theexternal radiation.

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FSF Spin-Valves: Comparison of Diferent ModelsNataliya Pugach1, M. Eschrig2, M. G. Flokstra3, T. C. Cunningham3, J. Kim4, N.Satchell4, G. Burnell4, P. J. Curran5, S. J. Bending5, C. Kinane6, A. Isidori2, J. F. K.

Cooper6, S. J. Langridge6, S.L. Lee31: Skobeltsyn Institute of Nuclear Physics, MSU, Moscow.2: University of London Egham, Surrey, TW20 0EX, UK.

3: School of Physics and Astronomy, SUPA, University of St.Andrews, KY16 9SS, UK.4: School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK.

5: University of Bath, Claverton Down, Bath, BA2 7AY, UK.6: ISIS, Rutherford Appleton Laboratory, Oxfordshire OX11 0QX, UK.


In 1999 the superconducting spin-valve was proposed theoretically [1,2], com-prising a superconducting (S) spacer layer separating two ferromagnetic (F) layers.For ideal operation, the in-plane supercurrent in the S layer can be controlled bythe mutual orientation of magnetization in the F layers. Initially the spin-valveefect was observed as a dependence of the critical temperature ( ) on the mag-netic coniguration, parallel (P) or antiparallel (AP) in such structures. However,the change between collinear and perpendicular coniguration may be muchmore pronounced than between P and AP alignment in a case of a strongly spin-polarized ferromagnet [3-5] due to appearance of the new channel for drainageof Cooper pairs from the S to the F layers related to appearance of the long-rangetriplet superconducting correlations (LRTC) [6,7].

We have calculated and observed [5] the angular dependence of the for FSFas well as SFF Co-Nb spin-valves. For both sample types (SFF and FSF) a large sup-pression of is found when the magnetizations are orthogonal, consistent withthe theoretical expectations for the drainage of singlet into the triplet LRTC chan-nel when the magnetization is non-collinear. This magnetization alignment maybe controlled by an external magnetic ield. The efect almost disappears whenswitching the spin-valve into a collinear state, when LRTC are absent. This showsthat LRTC in the ferromagnetic regions are a crucial ingredient contributing to theefect.

We have developed and compared diferent models for the description of theproximity efect between a usual superconductor and a strong ferromagnet. Suchspin-valves may serve as building blocks of spintronic devices and our investiga-tion provide a mechanism by which such devices might be realized.

We acknowledge the support of the EPSRC through Grants No. EP/J01060X,No. EP/J010626/1, No. EP/J010650/1, No. EP/J010634/1, and No.EP/J010618/1, support of a studentship supported by JEOL Europe and the ISIS

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Neutron and Muon Source, and the support of the RFBR via Awards No. 13-02-01452-a, and No. 14-02-90018 BEL-a.

References:1. A. I. Buzdin, A. V. Vedyayev and N. V. Ryzhanova, Europhys. Lett., 48 686-

691 (1999).2. L. R. Tagirov, Phys. Rev. Lett. 83 2058 (1999).3. P. V. Leksin, N. N. Garif’yanov, I. A. Garifullin, et al., Phys. Rev. Lett. 109

057005 (2012).4. A. Singh, S. Voltan, K. Lahabi, J. Aarts. arXiv:1410.4973 (2014).5. M. G. Flokstra, T. C. Cunningham, J. Kim, N. Satchell, G. Burnell, P. J. Cur-

ran, S. J. Bending, C. J. Kinane, J. F. K. Cooper, S. Langridge, A. Isidori, N.Pugach, M. Eschrig, S. L. Lee. Phys. Rev. B 91, 060501(R) (2015).

6. Ya. V. Fominov, A. A. Golubov, and M. Yu. Kupriyanov, JETP Letters 77 510(2003).

7. S. Mironov, A.I. Buzdin, Phys. Rev. B 89, 144505 (2014).

Peculiarities of DC-SQUIDs with Topologically Nontrivial BarrierIlhom Rahmonov � , Yu. M. Shukrinov � , K. Sengupta , R. Dawood �

: BLTP, Joint Institute for Nuclear Research, Dubna, Russia: Umarov Physical and Technical Institute, Dushanbe, Tajikistan

: Dubna International University for Nature, Society and Man, Dubna, Russia: Indian Association for the Cultivation of Science, Kolkata, India

: Cairo University, Giza, Egypt


Josephson junctions with topologically nontrivial barriers host Majoranabound states [1,2] Candidates with high potential for the detection and manipu-lation of the Majorana fermion [3] are superconducting quantum interference de-vices (SQUIDs) [4,5]. The appearance of Majorana bound states in superconduct-ing junctions enables tunneling of quasiparticles with charge across the junction,which doubles the Josephson periodicity � sin(��) [1].

We study in detail the behavior of DC-SQUIDs with topologically nontrivialbarriers and compare the results with the trivial case. The current voltage char-acteristics and the critical current dependence on the external magnetic lux forthe dc SQUID with trivial and nontrivial barriers are presented. We have shownthat so-called beating solutions at the resonance frequency [6] of DC-SQUID withnontrivial barriers shifts on√� in comparison with the case of trivial barriers. Weconsider that this fact might be used in the experimental detecting of Majoranafermions.

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References:1. L.Fu and C.L. Kane, Phys.Rev.Lett. 100, 096407 (2008).2. Y.Tanaka, T. Yokoyama, and N. Nagaosa, Phys.Rev.Lett. 103, 107002 (2009).3. E. Majorana, Nuovo Cimento 14, 171 (1937).4. L. Fu and C. L. Kane, Phys.Rev.B 79, 161408 (R) (2009).5. M. Veldhorst, C. G. Molenaar, C. J. M. Verwijs, H. Hilgenkamp, and A.

Brinkman, Phys.Rev.B 86, 024509 (2012).6. W. -D. Schmidt, P. Seidel, and S. Heinemann, Phys.Stat.Sol.(a) 91, K155

(1985)

Peculiarity of Resonance Between Fluxon and Plasma Wave inOne-Dimensional Parallel Array of Josephson Junctions

Kirill Rodin1, Ilhom Rahmonov2,3, Yury Shukrinov1,21: Dubna International University of Nature, Society, and Man, Dubna, Russia

2: BLTP, Joint Institute for Nuclear Research, Dubna, Russia3: Umarov Physical and Technical Institute, Dushanbe, Tajikistan


We present results of the numerical studies of the propagation of Josephsonluxon and electromagnetic waves in parallel arrays of Josephson junctions [1]. Aseries of resonances related to the locking between luxon rotation frequency andthe frequency of the radiated electromagnetic waves are observed in current volt-age characteristics of the arrays [2]. Peculiarity of the resonance between luxonand plasma wave and additional branch are found. The current voltage charac-teristics manifest the hysteretic behavior near the peculiarity. We investigate thevoltage-time dependence at diferent values of bias current and make a detailedFFT analysis of this dependence in current interval around the peculiarity. Wecompare our results with data presented in Refs. [1,2].

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Fig. 1

References:1. A. V. Ustinov, M. Cirillo, B. A. Malomed. Phys. Rev.B, 47, 8357 (1993).2. J. Pfeifer, A. A. Abdumalikov, Jr. M. Schuster, and A. V. Ustinov; Phys. Rev.

B, 77, 024511 (2008).

Quasi-Fermi Liquid: a Special State of One-Dimensional MatterAlexander Rozhkov

ITAE RAN, Moscow, Russia; MIPT, Dolgoprudnyi, Russia


It is well-known that the one-dimensional interacting fermions with marginal(in the renormalization group sense) interaction cannot be described in terms ofthe Fermi liquid. Instead, they present the phenomenology of the Tomonaga-Luttinger liquid. Imagine that for some one-dimensional fermionic systems themarginal part of the interaction is nulliied, and only irrelevant interactions re-main. It is argued in this presentation that such a fermionic liquid, which we pro-pose to call the quasi-Fermi liquid, exhibits the properties of both the Tomonaga-Luttinger liquid and the Fermi liquid. Similar to the Tomonaga-Luttinger liquid,the quasi-Fermi liquid does not support the inite-momentum quasiparticles; onthe other hand, the fermion occupation number demonstrates inite discontinuityat the Fermi energy, which is a hallmark feature of the Fermi liquid. A possibilityof realizing the quasi-Fermi liquid in trapped cold atoms is discussed.

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Superconducting Hybrids: From Sandwiches to Planar StructuresValery Ryazanov1,2, T.E. Golikova1,3, and V.V. Bolginov1,21: Institute of Solid State Physics, RAS, Chernogolovka, Russia

2: National University of Science and Technology ”MISiS”, Moscow, Russia3: Moscow Institute of Physics and Technology, Dolgoprudniy, Russia


Josephson hybrids based on superconductors (S), normal metals (N) and ferro-magnets (F) attract increasing attention in the last decade [1-7]. The most interest-ing and important observations were made mainly on S/F/S and S/F/N/S sand-wiches [3-7]. Among them it should be noted the implementation of �-junction(superconducting phase inverter) [3-5], observation of the spin-triplet supercon-ductivity [6], realization of SFS switches for ultra-low-power, high-density cryo-genic memorie [7,8]. Modern fundamental and applied researches make the ac-tual implementation and study of planar multiterminal S/F/N structures. PlanarJosephson S-(F/N)-S structures with complex bilayered (F/N) barriers were pro-posed recently in [9] and realized in [10]. The structure, which we studied in [10],included a Cu/Fe bilayer forming a bridge between two superconducting Al elec-trodes. The appreciable critical current was detected up to 120 nm of the bridgelength. It was observed a double-peak peculiarity in diferential resistance of theS-(N/F)-S structures at a bias voltage corresponding to the superconducting mini-gap. The splitting of the minigap was explained by the electron spin polarizationin the normal metal which was induced by the neighbouring ferromagnet. Ournew observations are related to quasiparticle and spin-injection to banks and bar-riers of planar Josephson junctions. First results were published in [11].

References:1. A. A. Golubov, M. Yu. Kupriyanov, and E. Il’ichev, Rev. Mod. Phys. 76, 411

(2004).2. A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).3. V.V. Ryazanov, V. A. Oboznov, A.Yu. Rusanov, A.V. Veretennikov, A.A.

Golubov, and J. Aarts, Phys. Rev. Lett. 86, 2427 (2001).4. T. Kontos, M. Aprili, J. Lesueur, F. Genet, B. Stephanidis, and R. Boursier,

Phys. Rev. Lett. 89, 137007 (2002).5. V. A. Oboznov, V. V. Bolginov, A. K. Feofanov, V. V. Ryazanov, and A. I.

Buzdin, Phys. Rev. Lett. 96, 197003 (2006).6. T. S. Khaire, M. A. Khasawneh, W. P. Pratt, Jr., and N. O. Birge, Phys. Rev.

Lett. 104, 137002 (2010).7. T. I. Larkin, V. V. Bol’ginov, V. S. Stolyarov, V. V. Ryazanov, I. V. Vernik, S. K.

Tolpygo, O. A. Mukhanov, Appl. Phys. Lett. 100, 222601 (2012).

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8. B. Baek, W. H. Rippard, S. P. Benz, S. E. Russek, and P. D. Dresselhaus, Nat.Commun. 5, 3888 (2014).

9. T. Yu. Karminskaya, A. A. Golubov, M. Yu. Kupriyanov, and A. S. Sidorenko,Phys. Rev. B 81, 214518 (2010).

10. T. E. Golikova, F. Hübler, D. Beckmann, I. E. Batov, T. Yu. Karminskaya, M.Yu. Kupriyanov, A. A. Golubov, and V. V. Ryazanov. Phys. Rev. B 86, 064416(2012).

11. T. E. Golikova, M. J. Wolf, D. Beckmann, I. E. Batov, I. V. Bobkova, A. M.Bobkov, and V. V. Ryazanov, Phys. Rev. B 89, 104507 (2014).

Long–Range Singlet Josephson Spin–Valve Efect in BallisticSFS Junction

Alexey Samokhvalov1, R. I. Shekhter2, A. I. Buzdin31: Institute for Physics of Microstructures RAS, GSP-105, Nizhny Novgorod, Russia2: Department of Physics, University of Gothenburg, SE-412 96 Göteborg, Sweden

3: Universit’e Bordeaux I, LOMA, UMR 5798, F-33400 Talence, France


We suggest a new way of control of the singlet Cooper pairs low through a su-perconductor/ferromagnet/superconductor (SFS) junction in the ballistic regime[1]. The method consists in creation of thin non-collinear domain ∼ �ℎ ≪ �(�ℎ � ℏ��ℎ) of the exchange ield ℎ near the center of a ferromagnetic weak linkusing a magnetic tip/probe (see Fig. 1).

Fig. 1: The schematic sketchof the SFS constriction under consideration: normal metal ballistic nanowire(NW) in contac with a superconductor (S) and a ferromagnetic insulator (FI).

The ield domain generated by the probe, induces a special scattering of Cooperpairs which corresponds to the spin-lip transition of electrons forming a pair. Asa result the scattered pair has a reversed spin arrangement with respect to the

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ixed exchange ield, and reversed total momentum. At a symmetric domainposition ( ≃ ) the total phase gain � between the electron- and hole-like partsof the wave function should be cancelled (� ∼ ( − )��ℎ → �) and the long–range singlet Josephson transport in SFS link becomes possible. It means that thepresence of a small region with a non-collinear exchange ield near the center of aferromagnetic weak link restores the critical current inherent to the normal metal.The long–range Josephson current (�) � sin�+ sin �� is very sensitiveto the position of the central domain, and the amplitude is negative at � .

This means that the spin-lip scatterer produces the�-shift efect and generatesa �-Josephson junction. With a displacement of the domain the SFS junctioncan be switched from � to � state (Fig. 2).

Fig. 2: The dependence of the long-range amplitudes of the irst(solid line) and the second (dashed line) harmonics of the current–phase

relation (�) on the shift � ( − )�� of the central domain with respect tothe weak link center. Dotted line shows the value of in absence of domain

The long–range behavior can be observed for a second harmonic in the current–phase relation (�) as well. Certainly, the contribution of the second harmonicin the current–phase relation (�) is small, except very close to the � − � transi-tion ( � �). At this � − � transition the contribution of the second harmonicbecomes dominant. For all considered cases we obtained the positive amplitudeof the second harmonic in the vicinity of these transitions, which means that theyoccur discontiguously by a jump between �− and �− phase states. The above phe-nomenon opens a way to control singlet Josephson current through ballistic SFSjunction. An additional functionality of the considered device can be achieved byelectric biasing of the magnetic gate via the ield efect.

This work was supported, in part, by French ANR grant ”MASH” and by theRussian Foundation for Basic Research (15-02-04116a).

References:1. A.V. Samokhvalov, R.I. Shekhter, A.I. Buzdin, Scientic Reports 4, 5671 (2014)

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Modeling of Intrinsic Josephson Junctions in High TemperatureSuperconductors

Yury ShukrinovBLTP, Joint Institute for Nuclear Research, and Dubna International University of Nature,

Society, and Man, Dubna, Russia


Short review of our recent results on modeling of Josephson junctions in hightemperature superconductors are presented. Particularly, a variation of longitudi-nal plasma wavelength under external electromagnetic radiation [1] and its exper-imental testing is discussed. We demonstrate the principal diference in the reac-tion of the system of coupled junctions to the external radiation in compare with acase of single Josephson junction [2,3]. The IV-characteristics of a Josephson junc-tion under external electromagnetic radiation show the devil’s staircase withindiferent bias current intervals [4,5]. It is found that the observed steps form veryprecisely continued fractions. We discuss an algorithm for the appearance anddetection of subharmonics with increasing radiation amplitude and demonstratethat the staircase structures registered in many well-known experiments and bysimulations form also the continued fractions. We study an efect of external ra-diation on the dynamics of Josephson junction shunted by an LC circuit. Whenthe Josephson frequency is equal to the frequency of the circuit, additional stableresonant circuit branches appear in the IV -characteristic of the junction. We showthat the amplitude dependence of the Shapiro step width crucially changes whenthe Shapiro step is on the resonant circuit branch. These efects might give veryimportant advantages for methods and technologies that exploit the response ofJosephson junctions to microwave ields [6].

References:1. Yu. M. Shukrinov, I. R. Rahmonov, M. A. Gaafar - Phys. Rev. B, 86, 184502

(2012).2. Yu. M. Shukrinov and H. Abdelhaiz- JETP Letters, 98, 551 (2013).3. Yu. M. Shukrinov, H. Azemtsa-Donfack, À.E. Botha. - Pisma v ZhETF, 101,

269 (2015).4. Yu. M. Shukrinov, S. Yu. Medvedeva, A. E. Botha, M. R. Kolahchi, A. Irie -

Phys. Rev. B, 88, 214515 (2013).5. Yu. M. Shukrinov, A. E. Botha, S. Yu. Medvedeva, M. R. Kolahchi, A. Irie -

Chaos, 24, 033115 (2014).6. Yu. M. Shukrinov, I. R. Rahmonov, K. V. Kulikov, P. Seidel - EPL, 110 , 47001

(2015).

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Detection of Single Abrikosov Vortex in a MicrowaveSuperconductor Resonator

Kirill Shulga1,2,3, V. O. Shkolnikov3,5, V. Chichkov1, N. Maleeva1, V. V.Ryazanov1,2,5, and A. V. Ustinov1,2,4

1: National University of Science and Technology (MISIS), Moscow, Russia2: Russian Quantum Center, Skolkovo, Russia

3: Moscow Institute of Physics and Technology, Dolgoprudny, Russia4: Physikalisches Institut, Karlsruhe Institut fuer Technologie, Karlsruhe, Germany

5: Institute of Solid State Physics, RAS, Chernogolovka, Russian Federation


Microwave coplanar resonators used in several experiments with supercon-ductor quantum bits(qubits). Qubits could afect on frequency and quality factorof resonators located near with them. Moreover, motion of magnet lux vorticesin superconductive ilm on chip have signiicant inluence on resonators param-eters. Also London penetration depth increasing with an increasing of externalmagnetic ield applied perpendicular to the sample, which in turn reduces ownfrequency of the resonator, and changes its quality factor. We have investigatephenomena of penetration single Abricosov vortex into the closed area of super-conductor formed by �� resonator. We have discovered hysteresis dependencein dynamic of single vortex interacting with pinning centers in thin supercon-ductor channel. Finally we showed phenomena of irreversible magnetization andcollecting of countable numbers of vortices in superconductor cavity.

Exchange Biasing of Diluted Ferromagnetic Alloy Films inSuperconducting Spin-Valves

Anatolie Sidorenko1, D. Lenk2, V.I. Zdravkov1,2,3, R. Morari1,4, A. Ullrich2, C.Müller2, H.-A. Krug von Nidda2, S. Horn2, L.R. Tagirov2,4, and R. Tidecks2

1: D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, MD2028Kishinev, Moldova

2: Institut für Physik, Universität Augsburg, D-86159 Augsburg, Germany3: Institut für Angewandte Physik, Universität Hamburg, D-20355 Hamburg, Germany

4: Solid State Physics Department, Kazan Federal University, 420008 Kazan, Russia


Exchange biasing of diluted ferromagnetic alloys (low- � weak ferromagnets)is a serious problem since basic condition � � � ( � and � are Curie and Neel

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temperatures of a ferromagnet and antiferromagnet, respectively), fulilled inconventional room-temperature spin-valves, is violated. The ability to exchangebias diluted ferromagnetic alloys is a keypoint for every kind of cryogenic spin-valve, Josephson or proximity, if low- � alloy is utilized as a functional materialin a superconductor-ferromagnet heterostructure. We present our recent ind-ing of strong exchange biasing of Cu41Ni59 weak ferromagnet by CoOx/Cu41Ni59interface with the aid of very thin cobalt sublayer adjacent to the CoOx an-tiferromagnet from the opposite side to the alloy layer. The magnetic prop-erties of Si(substr)/Si(bufer)/Co/CoOx/Cu41Ni59/Nb/Cu41Ni59/Si(cap) super-conducting spin-valve system are investigated by SQUID magnetometry, and twostrongly exchange biased signals are observed. The obtained results are comparedwith predictions of the domain state and spin-glass models of exchange bias.

Electrical Conduction in YBa2Cu3O7 – δ Single Crystals Under theConditions of Anionic Ordering in the Cu(1) O1 – δ Layers

M.V. Yarmolich1, N.A. Kalanda1, Nikolai Sobolev2,31: Scientiic-Practical Materials Research Centre, NAS, Minsk, Belarus2: Departamento de Física and I3N, Universidade de Aveiro, Portugal

3: National University of Science and Technology “MISiS”, Moscow, Russia


The critical temperatures of the superconducting transition inYBa2Cu3O7–δ (YBCO) depend on the concentration of the mobile oxygendistributed in the Cu(1) O1–δ chain planes. The maximum value of ∼ 9� Kis achieved at � � �� − �. This correlation is not mutually univocal, becausediferent values can be obtained for a given �, which is brought about byboth the concentration of the oxygen vacancies and their ordering in the anionsublattice of the YBCO crystal. This ordering can be considered as a methodof controlling the charge carrier concentration in square lattices of the Cu(2) O2crystal planes, thus inluencing the superconducting properties of the compound.

We have found that the increase of not always correlates with a change of theelectrical conduction anisotropy � �� at step-like and isothermal heat treatments.On the one hand, the increase in samples subjected to step-like annealing is ex-plained by the growth of the charge carrier concentration in the Cu(2) O2 planesand an enhancement of the interaction between the Cu(2) O2 and Cu(1) O1–δplanes. On the other hand, isochronous heat treatments at � �� − �8� Kand �(O ) � �� Pa promote a enhancement without changing �� . Asit seems, there is a limiting value of the electrical conduction anisotropy, belowwhich the latter does not correlate with variations in the YBCO crystals. It may

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be suggested that the proper mechanism of the inluence of the heat treatmentchanges at � �� − �8� K and �(O ) � �� Pa. In this case, the increase of

and of the orthorhombic distortion ( − ) occurs as a result of a contributionof the Cu(1) O1–δ chain layers to the electron density of states at the Fermi level.The Cu(1) O1–δ chain layers can be superconducting, which enables the existencein them of induced superconductivity due to the tunnelling of the Cooper pairsfrom the Cu(2) O2 planes.

The work has been supported by FCT of Portugal through the projectsUID/CTM/50025/2013, RECI/FIS-NAN/0183/2012 (FCOMP-01-0124-FEDER-027479), as well as by NUST „MISiS” through grant no. K3-2015-003.

Fluxon Scattering as a Tool for Detection and Manipulations withFlux Qubit States

Igor Soloviev1,2,3, N. V. Klenov4,1,2,3, A. L. Pankratov5,6,7, L. S. Revin5,6,7, E.Il’ichev8, A. V. Kuznetsov4, S. V. Bakurskiy4,3, O. V. Tikhonova4,1 and M. Yu.

Kupriyanov11: MSU, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia

2: Lukin Scientiic Research Institute of Physical Problems, Zelenograd, Moscow, Russia3: MIPT, State University, Dolgoprudniy, Russia

4: Lomonosov Moscow State University Physics Department, Moscow, Russia5: Institute for Physics of Microstructures of RAS, Nizhny Novgorod, Russia

6: Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia7: Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Russia

8: Leibniz Institute of Photonic Technology, Germany9: Institute for Nanotechnology, University of Twente, The Netherlands


We have considered relativistic luxon dynamics governed by the sine-Gordonequation and afected by short spatial inhomogeneities of the driving force andthermal noise. Developed analytical and numerical methods for calculationof luxon scattering at the inhomogeneities allowed us to examine the scatter-ing as a measurement tool for sensitive detection of superconducting lux qubitstates. Diferent measurement schemes based on the scattering were optimizedfor signal-to-noise ratio maximization. The scattering was also considered as atool for manipulation with the qubit states. Analysis of this type of manipula-tions with qubit states was performed in the frame of fully quantum descriptionboth analytically and numerically. In terms of the simplest model of two-levelsystem with magnetic moment we analyzed the possibility of fast magnetizationreversal on the picosecond timescale induced by unipolar magnetic pulse. In ad-dition, consideration of the magnetization reversal is fulilled in the framework

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of the macroscopic theory of the magnetic moment allowing the comparison andthe explanation of quantum and classical behavior.

Vortices at the Surface of a Normal Metal Coupled by ProximityEfect to a Superconductor

Vasiliy Stolyarov1,2,3, T. Cren1, Ch.Brun1, F.Debontridder1, I.Veshchunov2,O.Skryabina2,3, A.Baranov2, Bo Lu2,5, A.Golubov2,4, M.Yu.Kupriyanmov6,

D.Roditchev1,71: Institut des Nanosciences de Paris, UPMC and CNRS-UMR 7588, 75252 Paris, France

2: Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia3: Institute of Solid State Physics RAS, Chernogolovka, Moscow region, 142432 Russia

4: University of Twente, 7500 AE Enschede, Netherlands5: Department of Applied Physics,Nagoya University, Nagoya 464-8603, Japan

6: Skobeltsyn Institute of Nuclear Physics, MSU, Moscow, Russia7: LPEM-UMR8213/CNRS-ESPCI ParisTech-UPMC,75005 Paris, France


We report the experimental observation of vortices on the surface of a50nm-thick layer of Cu in the hybrid structure Cu/Nb with ultra-low temper-ature Scanning Tunneling Spectroscopy (STS). In the studied samples the non-superconducting Cu-layer acquires superconducting correlations due to the prox-imity e ect with 100 nm-thick superconducting Nb. To avoid the oxidation at Cu-surface and allow STS, the samples were ex-situ grown on SiO2/Si in the inversedorder, i.e. Cu was deposited directly on the substrate, Nb was deposited on Cu.Then the samples were introduced to the UHV STM chamber and cleaved in-situ.The structural analysis showed that upon cleavage the samples break at Cu/SiO2interface, thus exposing fresh Cu surface. The presence of the proximity efectat the Cu ilm surface was irst evidenced by observation of a proximity gap inthe tunneling conductance spectra d (�)�d� , in clear relation to the value of thesuperconducting gap of bulk Nb. The evolution of the proximity spectra with tem-perature was also studied in the range (0.3-4.2) K. Upon application of an externalmagnetic ield, spatial variations of the tunneling conductance spectra were ob-served. These variations appear in the detailed STS maps as round nm-size spots,in the centers of which the proximity gap vanishes. The density of spots rises con-tinuously with magnetic ield; it corresponds perfectly to the expected density ofAbrikosov vortices in Nb. We identify the observed spots as proximity inducedvortices in the normal Cu. On the basis of our STS data, we have determined thesize and shape of the proximity vortex cores, and evaluated the coherence lengthin Cu.

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Distribution of Condensate Functions in SuperconductingSpin-Valves

R.R. Gaifullin1, R.G. Deminov1, Lenar Tagirov1, T.Yu. Karminskaya2, M.Yu.Kupriyanov1,2,3, Ya.V. Fominov3,4, A.A. Golubov3,5

1: Kazan Federal University, Kazan, Russia2: Moscow State University, Moscow, Russia

3: Moscow Institute of Physics and Technology, Dolgoprudny, Russia4: L.D. Landau Institute for Theoretical Physics, Chernogolovka, Russia

5: University of Twente, Enschede, The Netherlands


We investigate the critical temperature of � � trilayers ( is a singlet su-perconductor, � is a ferromagnetic metal), where the long-range triplet supercon-ducting component is generated at noncollinear magnetizations of the � layers[1]. Earlier we demonstrated that in such structures can be a non-monotonicfunction of the angle � between magnetizations of the two � layers [2], contraryto the monotonic (�) behavior calculated for the � � superconducting spin-valve design [3]. It was shown recently [4] the existence of the anomalous depen-dence of the spin-triplet correlations on the angle� in �� structures. We examinethe spin-singlet and spin-triplet pairing distributions across the layers and theiramplitudes as a function of the angle � in the � � and � � superconductingspin-valve designs to clarify which one and why may show maximum spin-tripletpairing impact on the superconducting .

The support in parts by RFBR (grants No. 14-02-00793-a, 14-02-31002-mol_a,15-32-20362-bel_a_ved) and the Program of Competitive Growth of Kazan FederalUniversity is gratefully acknowledged.

References:1. F.S. Bergeret, A.F. Volkov and K.B. Efetov, Rev. Mod. Phys. 77, 1321 (2005).2. Ya.V. Fominov, A.A. Golubov, T.Yu. Karminskaya et al., JETP Lett. 91, 308

(2010).3. Ya.V. Fominov, A.A. Golubov and M.Yu. Kupriyanov, JETP Lett. 77, 609

(2003).4. T.Yu. Karminskaya, A.A. Golubov and M.Yu. Kupriyanov, Phys. Rev. B 84,

064531 (2011).

Recent Topic in Odd-Frequency Pairing: Consequences of BulkOdd-Frequency Superconducting States

Yukio Tanaka1,2, Ya. V. Fominov3,2, Y. Asano4,2, and M. Eschrig5

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1: Department of Applied Physics, Nagoya University, Nagoya, Japan2: Moscow Institute of Physics and Technology, Dolgoprudny, Russia

3: L. D. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia4: Department of Applied Physics & Center for Topological Science and Technology,

Hokkaido University, Japan5: Department of Physics, Royal Holloway, University of London, United Kingdom


Odd-frequency pairing has been studied after the prediction by Berezinskii [1].It has been theoretically clariied that odd-frequency pairing ubiquitously appearsin ferromagnet / superconductor junctions [2] and inhomogeneous systems [3,4].The relation between principal and induced pairing in superconducting junctionshas been clariied [3]. Andreev bound state, especially the edge state in uncon-ventional superconductor, is expressed by odd-frequency pair amplitude [3].

One of the remarkable feature of the odd-frequency pairing is the anomalousproximity efect in difusive normal metal (DN) / superconductor junction, wheredensity of states of quasiparticle in DN has a zero energy peak[5]. Furthermore, ithas been revealed that Majoirana fermion which appears as an edge state of topo-logical superconductor can be regarded as an odd-frequency pairing [6]. Theselocally induced odd-frequency pair amplitudes show paramagnetic Meissner re-sponse, and induced odd-frequency pair amplitude can be called as an odd-parastate [3, 9]. If odd-para state is generated as a bulk superconducting state, it arisesthe problem of stability of superconductivity. Recently, odd-frequency pairingthat exhibits diamagnetic Meissner response (”odd-dia state”)[7-8] was suggestedin order to resolve stability issues arising in an odd-para state.

We note that if we admit the realization of ”odd-dia state” Cooper pairs areclassiied into eight classes in terms of their symmetries and magnetic properties.Anomalous magnetic properties of the induced subdominant components can beprobed by studying the Meissner efect. Assuming the existence of an odd-diastate (due to a proper retarded interaction), we study its co-existence with an odd-para state. Calculating the superluid density of the mixed odd-para/odd-diastate and the Josephson current between the odd-para and odd-dia states, we indthat the expressions for the currents in both cases have non-vanishing imaginarycontributions and are therefore unphysical[10]. We show that a realization of theodd-dia state implies the absence of a Hamiltonian description of the system, andsuggest that there exists no physically reasonable perturbation that could give riseto the spontaneous symmetry breaking necessary for an actual realization of theodd-dia superconducting state.

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Tabl. 1: Table Eight possible class of pairing symmetry.ESE (even-frequency spin-singlet even-parity), ETO(even-frequency spin-tripletodd-parity), OTE (odd-frequency spin-triplet even-parity), OSO (odd-frequencyspin-singlet odd-parity). Para (Dia) means the response to Meissner efect.

References:1. V. L. Berezinskii: JETP Lett. 20 287 (1974).2. F. S. Bergeret, A. F. Volkov, and K. B. Efetov: Phys. Rev. Lett. 86 4096 (2001).3. Y. Tanaka, M. Sato and N. Nagaosa, J. Phys. Soc. Jpn. 81 011013(2012), Y.

Tanaka, et al, Phys. Rev. Lett. 99 037005 (2007).4. M. Eschrig, et al, J. Low. Temp. Phys. 147, 457 (2007).5. Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98, 037003 (2007).6. Y. Asano and Y. Tanaka, Phys. Rev. B, 87 104513 (2013).7. H. Kusunose, Y. Fuseya, and K. Miyake, J. Phys. Soc. 80, 054702 (2011).8. D. Solenov, I. Martin, and D. Mozyrsky, Phys. Rev. B 79, 132502 (2009).9. Y. Asano, Y. V. Fominov, Y. Tanaka, Phys. Rev. B 90 094512 (2014).

10. Y. V. Fominov, Y. Tanaka, Y. Asano, M. Eschrig, Phys. Rev. B 91 144514(2015).

Prospective Applications of Superconducting andSuperconducting-Ferromagnetic Heterostructures

Igor VernikHYPRES, Inc., 175 Clearbrook Road, Elmsford, NY 10523, USA


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As energy eiciency became the new limiting factor deining processor per-formance, a simple scaling of conventional CMOS devices is not expected to leadto the next generations in high performance computing (HPC). Superconductingsingle lux quantum (SFQ) Josephson devices with fast (∼ � ps) and low-energy(∼ ��− � J) switching coupled with fast and lossless interconnects are viewed asa potential alternative technology. The SFQ logic power dissipation is furtherreduced (∼ �� ) with an introduction of energy-eicient SFQ logic, making itviable contender to implement next generation HPC, cryogenic sensor image pro-cessors, and high-end instrumentations even after taking into account the cry-ocooling overhead of ∼ �� W/W for �� K.

Superconducting ferromagnetic (SF) heterostructures ofer a new dimensionto superconducting electronics enabling previously unattainable properties andfunctionalities. Relatively near term applications are sought when SF devices arehybridized with conventional Josephson junctions (JJ) augmenting and enhancingthe high speed and low power dissipation of JJ-based SFQ electronics. The highlydesired impact is expected in the development of dense, high capacity randomaccess memories which so far has been proven to be diicult for conventional JJelectronics.

In this presentation, recent signiicant advances in energy-eicient logic aswell as progress in resolving long standing problems to develop cryogenic mem-ory and high speed data link for low power SFQ circuits will be reviewed.

Efect of Van Hove Singularities on the d-Form Factor ChargeOrdering in Cuprate High-Temperature Superconductors

Pavel VolkovRuhr University Bochum, Germany


We investigate the efect of Van Hove singularities on the d-form factor chargeordering in cuprate high-temperature superconductors. Assuming spin luctua-tion exchange interaction we show that if the antinodal portions of the Fermi Sur-face are close enough to the Van Hove singularity, the leading instability is a � �Fermi Surface distortion. Using the data from experiments [1,2] we show thatunderdoped BSCCO indeed satisies our assumptions. As this type of symmetrybreaking does not open a gap, we show that at lower temperature this leads to a d-form factor charge density wave formation with wavevector along one of the Bril-louin Zone axes. The magnitude of the wavevector is determined self-consistentlyand can be substantially larger, then the wavevector, connecting antinodal points

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of the Fermi Surface. This is in accord with recent experiments, showing that d-form factor charge density wave order with wavevectors along Brillouin zone axesis a ubiquitous feature of hole-doped cuprate superconductors [3-6].

References:1. M. Hashimoto et al., Nat. Phys. 6, 415 (2010); Rui-Hua He et al., Science 331,

1579 (2011).2. W. D. Wise et al., Nat. Phys. 4, 696 (2008).3. E. Blackburn et al., Phys. Rev.Lett. 110, 137004 (2013).4. A. J. Achkar et al., Phys. Rev. Lett. 109, 167001 (2012).5. Fujita et al., PNAS 111, 30, 3026 (2014).6. Comin et al., Science 347, 1335 (2015).

Crossed Surface Flat Bands in Weyl Semimetal SuperconductorsKeiji Yada, Bo Lu, Masatoshi Sato and Yukio Tanaka

Nagoya University


Weyl semimetals (WSMs) are three-dimensional materials that support pairsof bulk gapless points which is called Weyl points.[1-8] One of the important char-acter of the Weyl points is the appearance of the Fermi arc state as a surface state,which connects two Weyl points.[2] It is also known that the breaking of the timereversal symmetry or the inversion symmetry is necessary to realize the WSM.[4]With the slight doping, WSMs have disconnected Fermi surfaces, each of whichsurrounds one of the Weyl points. The superconducting state of this doped WSMhas been studied for uniform (BCS state) and nonuniform (FFLO state) Cooperpairing. Interestingly, the uniform superconducting state has nodes which arecharacterized by the topological invariants.

In this talk, we present the surface state of the superconducting doped WSMwith uniform s-wave pairing.[9] We ind that the Fermi arc surface state remainsin the superconducting state without gap opening. Owing to this, the surface An-dreev Bound state (ABS) has a twisting dispersion. Then, the zero energy state ofthe ABS becomes crisscross in the surface Brillouin Zone. We also ind the con-ditions for the realization of the crossed lat bands. The irst is the time-reversalbreaking WSM. The second is the uniform pairing. The third is the magnetic mir-ror relection symmetry which is the product of the time-reversal and mirror re-lection symmetry. If these three conditions are satisied, there is the possibilityof the existence of the lat bands.

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(a) Energy dispersion�( � ) of the surface ABS inside the projected Fermi surface. (b) Quasiparticlespectra function at zero energy. Dashed line denotes the projected Fermi surface.

References:1. S. Murakami, New J. Phys. 9, 356 (2007).2. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83,

205101 (2011).3. G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Phys. Rev. Lett. 107, 186806

(2011).4. A. A. Burkov and L. Balents, Phys. Rev. Lett. 107, 127205 (2011).5. W. Witczak-Krempa and Y. B. Kim, Phys. Rev. B 85, 045124 (2012).6. G. Chen and M. Hermele, Phys. Rev. B 86, 235129 (2012).7. H.-J. Kim, K.-S. Kim, J.-F. Wang, V. A. Kulbachinskii, K. Ogawa, M. Sasaki,

A. Ohnishi, M. Kitaura, Y.-Y. Wu, L. Li, I. Yamamoto, J. Azuma, M. Kamada,and V. Dobrosavljevi´c, Phys. Rev. Lett. 110, 136601 (2013).

8. T. Morimoto and A. Furusaki, Phys. Rev. B 89, 235127 (2014).9. B. Lu, K. Yada, M. Sato, and Y. Tanaka, Phys. Rev. Lett. 114, 096804 (2015)

Strange Metals, Fermion Signs and EntanglementJan Zaanen

Instituut Lorentz for Theoretical Physics, Leiden University, The Netherlands


The strange metals as observed in high superconductors and other cor-related electron systems are arguably the greatest enigma of condensed matterphysics. The diiculties are rooted in the fundamentals of physics: the lack of a

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general mathematical mathematical framework to deal with strongly interactingfermions at inite density, the “fermion sign problem”. The holographic dualityas discovered in string theory is the irst method yielding a precise descriptionof non-Fermi liquids [1]. These holographic strange metals are suggestively simi-lar to the laboratory variety, at the same defeating the basic principles of bosonicield theory. These are quantum critical phases with scaling properties alien tothose computable with conventional methods. Remarkably their entanglemententropies demonstrate that their ground states are more densely entangled thandeemed possible. I will present some irst indications that this is rooted in thesign structure. Using the so-called nodal surface (zero’s of the wavefunction) asa measure, this fermionic entanglement structure can be addressed in a geomet-rical language. The nodal surface of a Fermi liquid is characterized by a scale butusing a particular Ansatz a quantum critical state can be described characterizedby a fractal nodal surface. We show that such states are characterized by entangle-ment entropies, which are strikingly similar as to those of the holographic strangemetals.

References:1. J. Zaanen, Y.-W. Sun, Y. Liu, K. Schalm, Holographic Dualtity for Condensed

Matter Physics (Cambridge Univ. Press, in press, 2015)2. F. Kruger and J. Zaanen, Phys. Rev. B. 78, 035104 (2008)3. N. Kaplis. F. Kruger and J. Zaanen, unpublished.

Abstracts

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VenueVenueConference Place:

Moscow, Leninskiy prospekt 4, MISIS. GPS: 55.728414, 37.608737.

Venu

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Presenting Author IndexAkzyanov, 14Asano, 15Averkin, 15

Bakurskiy, 16Batov, 17Bobkova, 17Bolginov, 18Burmistrova, 19Buzdin, 20

Devyatov, 21

Efetov, 23EfetovD, 22Efremov, 24Eremin, 24

Ferraz, 25

Goldobin, 25Golovchanskiy, 26Golubov, 27

Ikegaya, 28

Kagan, 29Karpov, 30Klenov, 31Krasnov, 32Kupriyanov, 33Kuzmicheva, 35

Larionov, 36

Maiti, 37Matveenko, 38Melnikov, 38Mironov, 39Moor, 40Morr, 40Mukhin, 41

Nashaat, 42

Pugach, 43

Rahmonov, 44Rodin, 45Rozhkov, 46Ryazanov, 47

Samokhvalov, 48Shukrinov, 50Shulga, 51Sidorenko, 51Sobolev, 52Soloviev, 53Stolyarov, 54

Tagirov, 55Tanaka, 56

Vernik, 57Volkov, 58

Yada, 59

Zaanen, 60

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Abstracts book ismn-2015

Science

Transcript of Abstracts book ismn-2015