New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro...
-
date post
19-Dec-2015 -
Category
Documents
-
view
212 -
download
0
Transcript of New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro...
![Page 1: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/1.jpg)
New roads opening in the field of Superconducting Materials after the
discovery of MgB2
Sandro Massidda
Physics Department University of Cagliari
[email protected]://www.dsf.unica.it/~sandro/
![Page 2: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/2.jpg)
Outline
•Ingredients of conventional superconductivity: electrons and phonons. •The electron-phonon interaction in real materials. •Key concepts: Kohn anomaly, two-gap superconductivity, Fermi surface nesting, covalently bonded metals. •Applications to real materials: MgB2, CaSi2, intercalate graphite
CaC6 , alkali under pressure
•Most superconductors have been discovered by chance!•Can we do better? •Basic elements can be found in many SC and can serve as a guide in the search
![Page 3: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/3.jpg)
Origin of “conventional” superconductivity: phonons produce an attraction among electrons (Cooper pairs)
Lattice deformation
Classical view of how a lattice deformation by a first electron attracts the second one
Overscreening of e-e repulsion by the lattice
![Page 4: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/4.jpg)
First ingredient: Energy bands. Example of Cu
d bandsNarrow, filled
s bands nearly
parabolic: free-electron
Symbols are from experiments
Band dispersion from Bloch theorem carries the information on chemical
bonding Similarity: bonding &
anti-bonding molecularorbitals
k (r l) k (r)ei k l
k
![Page 5: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/5.jpg)
An interesting material: MgB2
Tc=39.5 K
Isoelectronic to graphite, why so different?
B planes
Mg planes
![Page 6: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/6.jpg)
sp2
Energy bands of MgB2
3D bands (strongly dispersed along -A (kz))
2D bands (weakly dispersed along -A)
k=(kx;ky;) (0,0,kz ) (kx;ky;/c)
s
bonding (px,py)
bonding & antibonding
(pz orbitals)
![Page 7: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/7.jpg)
E l e c t r o n i c p r o p e r t i e s o f MgB2
2-D-bonding bands3-D bands
B
B
BStrong covalent bonds
![Page 8: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/8.jpg)
A
Mg Mg
B
0,0, / ck
B
k 0
-+
++
Dispersion and bonding: bands
-
![Page 9: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/9.jpg)
•Different dispersion along kz: 2D vs 3D
MgB2
Graphite
The presence of cations is crucial to get holes.
holes are the origin of superconductivity
![Page 10: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/10.jpg)
Fermi surface of MgB2
B px and py ( )
B pz ( )
The FS is the iso-energy surface in k-space separating filled and empty states
![Page 11: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/11.jpg)
Second ingredient: Phonons
s atom
cartesian component
l lattice point
Lattice deformation:
detCss ' '(q)
M sM s '
2 (q) 0
Rls R0ls us (q)eiqRl
3Nat phonon branches at each wave vector q
Force constants contain the response of the electrons to ionic displacement: fundamental ingredient
k
M 2Analogy with elementary
mechanics:
![Page 12: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/12.jpg)
First-principles calculations vs experiments
![Page 13: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/13.jpg)
Source of electron-electron attraction
Virtual phonon
qk k’
k+q k’-q
![Page 14: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/14.jpg)
BCS theory: superconducting gap
k Vkk '
k '
2 k '2 k '
2k ' tanh
k '2 k '
2
2kBT
Ek k2 k
2 excitation energies
2hDe 1
k
≈2
Tc 1.14e 1
2kBTc
3.52
Coherence length
Exponential dependence on the coupling
![Page 15: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/15.jpg)
ELIASHBERG theory (1960):
• attractive electron-phonon interaction:
22 ( )d
F
Eliashberg Spectral Function 2F() describes the coupling of phonons to electrons on the Fermi Surface
trTConnection to normal state electrical resistivity :
![Page 16: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/16.jpg)
Pb and MgB2 Eliashberg functions
Pb MgB2
=1.62 Tc=7.2 K =0.87 Tc=39.5 K
Low phonon frequencies Large phonon frequenciesStill, CaC6 has larger and similar but Tc=11.5 K !!!
![Page 17: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/17.jpg)
McMillan Equation
T
c1.2
e 1.04
1 * (10.62 )
represents the Coulomb repulsion and is normally fitted to experimental Tc
N(EF ) I 2
M ph2
N(EF) electronic density of statesI e-ph interaction M nuclear massph average ph. frequency
Exponential dependence
![Page 18: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/18.jpg)
Results of theoretical calculations for elemental superconductors: comparison with experiment
TcT=0 gap at EF
M. Lüders et al. Phys. Rev. B 72, 24545 (2005)M. Marques et al. Phys. Rev. B 72, 24546 (2005)A. Floris et al, Phys. Rev. Lett. 94, 37004 (2005)G. Profeta et al, Phys. Rev. Lett. 96, 46003 (2006)
Cagliari Berlin L’Aquila collaboration
![Page 19: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/19.jpg)
Phonon density of states Spectral function 2F()
MgB2 superconductor, AlB2 no
2
2 F( )
d
Comparable phonon DOS, very different 2F()
![Page 20: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/20.jpg)
Phonons in MgB2
Anomalously low frequency E2g branch (B-B bond stretching)
E2g
B1g
![Page 21: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/21.jpg)
Large coupling of the E2g phonon mode
with hole pockets (band splitting)
E2g=0.075 eV
≈ 1-2 eV !!!
![Page 22: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/22.jpg)
Phonon life-time
As soon as holes disappear with e-doping, superconductivity disappearsThe width of Raman lines are proportional to the phonon inverse life-time. The difference between MgB2 and AlB2 indicates the different electron-phonon coupling in these two materials
AlB2 not SCMgB2 SC
Electron doping destroys SC
![Page 23: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/23.jpg)
Kohn anomaly: LiBC, isoelettronic to MgB2 (Pickett)
Stoichiometric compound is a semiconductor
Metallic upon dopingKohn anomalyHigh Tc predicted
Unfortunately not found experimentally
Strong renormalization of phonon frequencies
phon
on f
requ
ency
![Page 24: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/24.jpg)
Kohn anomaly
The electronic screening is discontinuous at 2kF (log singularity in the derivative of the response )
For q>2kF it is not possible to create excitations at the small phonon energy
For q<2kF the electronic screening renormalizes the phonon frequency
2 Fq k
d q
dq
q > 2kF
FS
q < 2kF
A Kohn anomaly lowers the energy of E2g phonons in MgB2
2-dimensionality increases the effect
![Page 25: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/25.jpg)
Two band model for the electron phonon coupling (EPC)
• stronger in bands due to the
coupling with E2g phonon mode• Experiments show the existence of two gaps: and .
Two band model:experimental evidenceR. S. Gonnelli, PRL 89, 247004 (2002)
Fermi surface
Specific heat: evidence of 2 gaps
![Page 26: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/26.jpg)
Two-gap structure associated with and bands
Tunnellingexperiments
![Page 27: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/27.jpg)
Two band superconductivity
Tc depends on the largest eigenvalue of the inter- and intra- band coupling constants, nm and not on the average
![Page 28: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/28.jpg)
Impurities in two-gap superconductors
have a pair-breaking effect as magnetic impurities in single-gap SC
Unfortunately, the experimental situation is not so clear
![Page 29: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/29.jpg)
CaGa2 CaSi2
CaSi2 becomes Superconductor under pressure, Tc around 14 K
CaGa2-xSixParent structures to MgB2
Tc
![Page 30: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/30.jpg)
CaSi2: phase transitions and superconductivity
Frozen-in B1g phonon: trigonal structure due to instability of bands
trT at high T
Trigonal MgB2
![Page 31: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/31.jpg)
CaSi2: instability of bands; sp2 sp3
Amplitude of trigonal distortion vs pressure and band filling
CaSi2
KSi2
Lowered frequencies in SC MgB2. CaBeSi?
Large splitting at EF upon distortion
DOS
![Page 32: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/32.jpg)
CaBeSi
bands at EF
![Page 33: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/33.jpg)
N. Emery et al. Phys. Rev Lett. 95, 087003 (2005)
Intercalate graphite: CaC6 Tc=11.5 K
The highest Tc among intercalated graphite compounds (normally Tc < 1 K)
![Page 34: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/34.jpg)
CaC6
Amount of Ca contribution
FS
Ca FS
C FS
![Page 35: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/35.jpg)
Phonons in CaC6: 21 modes
Very high frequencies but also low frequency branches
![Page 36: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/36.jpg)
CaC6: gap and orbital character
Gap k over the Fermi surface
Orbital character
k
![Page 37: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/37.jpg)
Superconductivity under pressure
29 elements superconducts under normal conditions
23 only under pressure: Lithium is the last discovered
![Page 38: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/38.jpg)
Tc(P) is a strongly material-dependent function*
* C. Buzea and K. RobbieSupercond. Sci. Technol. 18 (2005) R1–R8
![Page 39: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/39.jpg)
Aluminium under pressure……
270 GPa
Bonds get stiffer, frequencies higer …Al becomes a normal metal
N (EF ) I 2
M ph2
![Page 40: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/40.jpg)
Alkali metal under high pressure: many phase transitions
![Page 41: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/41.jpg)
hR1
CI16
7
39
42
…
…
…
0 9R
fcc
Lithium is a superconductor under pressure
![Page 42: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/42.jpg)
K
Li
Charge on p states
Charge on d states
27 GPa
30 GPa
Electron states of Li and K under pressure
![Page 43: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/43.jpg)
Phonon dispersion in Li: softening and stiffening
0 GPa
26 GPa
0 GPa
26 GPa
![Page 44: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/44.jpg)
Why?
Phonon softening and lattice instability
Increasing the pressure a lattice instability driven by the Fermi surface nesting increases the electron-phonon coupling
q
Pieces of Fermi surface connected by the same wave-vector q
q
Imaginary frequency: instablility
![Page 45: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/45.jpg)
Orbital character at EF and superconductivity
Li
d character
p character
![Page 46: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/46.jpg)
Electron-Phonon Coupling
Pressure
Stiffer bonds (higher ’s) but higher coupling at low
![Page 47: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/47.jpg)
Theoretical predictions
![Page 48: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/48.jpg)
Summary
• I presented an essential description of the properties
and SC mechanisms in a few important materials
• Each real material has plenty of interesting physics
•SC needs material-adapted understanding where similar mechanisms can act in very different ways
![Page 49: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/49.jpg)
A15 Compounds
Nb3Sn Tc=18 Kit could be a Multigap SC
Guritanu et.al. PRB 70 184526 (2004)
![Page 50: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/50.jpg)
Lattice distortions in Nb3SnFree-energy of cubic and tetragonal
c
a 1
Softening of elastic constant
Softening of optical phonon mode
V3Si
Nb3Sn
![Page 51: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/51.jpg)
Lattice distortions in A15
![Page 52: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/52.jpg)
Band structure of Nb3Sn
Large peak at EF
![Page 53: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/53.jpg)
Concepts in ELIASHBERG theory:
Superconductivity results from the competition
of opposite effects:
1 lnel el FS
F
D
VE
• repulsive Coulomb interaction (Morel Anderson):
The difference between electron (h/EF) and nuclear (1/D) time
scales reduces the coulomb repulsion (retardation)
![Page 54: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/54.jpg)
Impurities in two-gap superconductors Irradiation by neutrons (Putti et al)
Only in a C-doped sample the merging has been observed at 20 K (Gonnelli et coworkers)
![Page 55: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/55.jpg)
x = 0
x = 0.25
x = 0.33
x = 0.5
Mg1-xAlxB2
Electronic properties of Al-doped MgB2
![Page 56: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/56.jpg)
Electron-phonon spectral function
2F()
![Page 57: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/57.jpg)
Bands of CaSi2 in the ideal and distorted (full lines) structures
![Page 58: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/58.jpg)
Spectral function of Nb3Sn from tunnelling
Many different results with many different values, ranging from =1.08 to 2.74!
![Page 59: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/59.jpg)
Non-magnetic impurities: Anderson theorem
In the presence of disordered impurities the wave-vector k is not a conserved quantity: electrons cannot sneak anymore as Bloch suggested, if the potential is not periodic
However, the impurity potential being static, V(r, t ), we still have stationary states:
k n
We can form Cooper pairs by time-reversal degenerate states
k , k
n ,n*
Important physical conclusion: Tc does not change in a
significant way due to the presence of impurities!
![Page 60: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/60.jpg)
Impurities: experiments
Tc proportional to the low temperature resistivity, related to impurities induced by irradiation.
![Page 61: New roads opening in the field of Superconducting Materials after the discovery of MgB 2 Sandro Massidda Physics Department University of Cagliari sandro.massidda@dsf.unica.it.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d2b5503460f94a002a3/html5/thumbnails/61.jpg)
Magnetic impurities: Gorkov-Abrikosov theory
Magnetic impurities split the energy of states with spin and pair breaking effect
Important physical conclusion: Tc is strongly
depressed by the presence of magnetic impurities!
Ni
d
d The presence of a static magnetic moment is incompatible with conventional superconductivity