Competing interactions and theories of cuprate ...€¦ · Sasha Alexandrov Loughborough...
Transcript of Competing interactions and theories of cuprate ...€¦ · Sasha Alexandrov Loughborough...
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Sasha Alexandrov
Loughborough University, United Kingdom
Competing interactions and theories of cuprate superconductors
Quantifying the electron-phonon Froehlich interaction
Polaronic and bipolaronic superconductivity
Evidence for Real-Space pairs in Hole Doped CupratesHc2
Specific heat anomaly
Lorentz number
Normal state diamagnetism
Parameter-free fit of Tc
Superconducting gap and pseudogap
Conclusion
Some recent publications:
A. S. Alexandrov and J. T. Devreese, Advances in Polaron Physics (Springer, Berlin 2009).
A. S. Alexandrov and A. M. Bratkovsky, Key pairing interaction in layered doped ionic insulators, Phys. Rev. Lett. 105 226408 (2010)
A. S. Alexandrov and J. Beanland, Superconducting gap, normal state pseudogap and tunnelling spectra of bosonic and cuprate
superconductors, Phys. Rev. Lett. 104, 026401 (2010)
J. P. Hague, P. E. Kornilovitch, J. H. Samson, and A. S. Alexandrov, Superlight small bipolarons in the presence of a strong
Coulomb repulsion, Phys. Rev. Lett. 98, 037002 (2007)
A. S. Alexandrov, Normal state diamagnetism of charged bosons in cuprate superconductors, Phys. Rev. Lett. 96, 147003
(2006)
Strong-coupling superconductivity beyond BCS and the key pairing interaction in
cuprate superconductors
CMMP2010
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Acknowledgment:
Sasha Andreev
Alex Bratkovsky
Victor Kabanov
Jozef Devreese
Pavel Kornilovitch
Peter Zhao
Joanne Beanland
Jim Hague
Tom Hardy
Chris Dent
Kim Reynolds
John Samson
P.L.Kapitza Institute for Physical Problems
Supported by EPSRC, Leverhulme Trust and the Royal Society (UK)
Universiteit Antwerpen
http://www.ua.ac.be/http://www.ua.ac.be/
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Tc>100K?
(1986)
Theories of high-Tc
Bardeen-Cooper-Schrieffer (BCS)
Theory (1957) Bipolaron theory (1981,1983)
e-ph interaction
BCS excitonic
BCS plasmonic
BCS magnetic
BCS kinetic e-e Coulomb repulsionResonating-valence-bond (RVB)
theory (1987), Hubbard U-tJ
Weak electron-pairing
correlations
Real space tightly bound 2e pairs
Electron decays into a singlet charge e
“holon” and spin-½ “spinon”
2e, S=0,1
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Low Fermi energy: pairing is individual
2D electrons: EF=d ħ2c2 /(4ge2 l2H)
Pairing is individual (i.e. real-space pairing) since
EF 150 nm, so
EF < 50 –100 meVin underdoped and even in optimally and
some overdoped cuprates
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Magneto-oscillations: low Fermi energy
N. Doiron-Leyraud et al., Nature 447, 565 (2007).
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Y Ba 2Cu 3 O6.5 Y Ba2 Cu4 O8
E. A. Yelland et al., arXiv:0707.0057
kF ≈ 1.3 nm -1,
m* ≈ 2me
l≈16 nm,
kFl ≈20,
Hc2(0)≈50 Tesla,
Small electron FS pocket
m*≈3me,
EF≈ 30 meV < ħω (60 -80 meV)
A. F. Bangura et al., arXiv:0707.4461.
l≈9 nm
kFl≈10
C. Jaudet et al., arXiv:0711.3559
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Ep=(e-1 - e0-1 )Sq2pe
2/q2
2 Ep>>J=4t2/U ≈0.15 eV
ASA and A.M. Bratkovsky, Phys. Rev. Lett. 84 2043 (2000)
DOS
E
m
d-bandd-bandp-band
Eopt
Band structure and essential interactions in cuprates
La2CuO4 : Ep=0.65 eV
with e=5, and e0=30
La2MnO3 : Ep=0.88 eV
with e=3.9, and e0=16
The chemical potential remains inside the charge-transfer gap at finite doping:I. Bozovic, G. Logvenov, M. A. J. Verhoeven, P. Caputo, E. Goldobin, and T. H. Geballe, Nature (London) 422, 873 (2003)
Theory:
LDA+U :V.I. Anisimov et al.
J. Phys.: Condens. Matter 9, 767 (1997).
Cluster diagonalisations:
S.G. Ovchinnikov et al., Physica B359,
1168 (2005)
Site-slective experiments:M. Merz et al.
Phys. Rev. Lett. 80, 5192 (1998).
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Hubbard U and t-J “catastrophe”
J. Phys. Soc. Jpn. 76, 113708 (2007)
et al.
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Weak-coupling Hubbard-Fröhlich model
VMC result (T. M. Hardy, J. P. Hague, J. H. Samson, and ASA, PRB 79, 212501 (2009))
84 electrons on 10x10 square lattice
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Isotope effect on the supercarrier mass
ASA, Phys. Rev. B46, 14932 (1992):
m*, m** =mexp(g2), am*=d ln m*/dlnM=0.5 ln(m*/m)
Connection with the isotope effect on Tc: a=-dlnTc/dlnM=am*[1-Z/(l-mc)],
Z=m/m*
Experiment:
G. Zhao and D. E. Morris,
Phys. Rev. B 51, 16487 (1995);
G. Zhao, M.B. Hunt, H. Keller,
and K.A. Muller,
Nature 385, 236 (1997);
R. Khasanov et al.,
Phys. Rev. Lett. 92, 057602 (2004).
Polaronic multi-band model:A. Bussmann-Holder, H. Keller, A.R. Bishop,
A. Simon, R. Micnas, and K.A. Muller,
Europhys. Lett. 72, 423 (2005).
YBa2Cu3O7-δ
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Electron-Phonon Interactions in Superconducting La1.84Sr0.16CuO4 Films
Heejae Shim, P. Chaudhari, Gennady Logvenov, and Ivan Bozovic
Phys. Rev. Lett. 101, 247004 (2008)
Phonons in tunnelling spectra of cuprate superconductors
also in :
http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://link.aip.org/link?prl/101/247004http://prola.aps.org/search/query
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Phys. Rev. B77, 092508 (2008)
Non-adiabatic first-principle results:
Thomas Bauer and Claus Falter
Phys. Rev. B 80, 094525 (2009)
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Ultrafast pump/probe determination of electron-phonon coupling
Phys. Rev. Lett (2010), in print
λ ~ 0.5 or higher (LSCO)
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Froehlich EPI is the key pairing interaction in layered doped ionic insulators
A.S. A. and A. M. Bratkovsky,
Phys. Rev. Lett. 105 (2010) 226408
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Rsc=0,1,3,∞
QMC polaron mass
(Alexandrov& Kornilovitch, PRL 1999; Spencer et al. PRB
2005)
2D,ω=0.5t
1D
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Ground state of strongly-correlated electrons and phonons
EF
λ < 0.5,
Fermi/BCS liquid
εF
D
W=De-g2
λ >0.5, v > 0
Polaronic Fermi liquid
(ASA, 1983)
λ >1, v < 0,
Bipolaronic Bose liquid
ASA and Ranninger (1981)
Ep
Δ/2
Breakdown of the Migdal-Eliashberg approximation at λ > 0.5
since λћω/εF > 1 (ASA,1983)
(λ=2Ep/D, εF=EFexp(-g2), g2~Ep/ћω)
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(Bi)polaronic superconductivity in cuprates (ASA, 1987)
λ > 0.5, λ – μc > 0
Strong electron correlations help form small
lattice polarons at even lower coupling with
phonons [Fehske and Trugman (2008)
Mishchenko and Nagaosa (2008)]
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Bipolaron model of cuprates (Alexandrov (1987))
Apex bipolaron (Alexandrov (1996),
Catlow et al. (1991,1998))In-plane bipolarons (ASA & Mott (1993))
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Superlight small bipolarons
QMC results (Hague et al. PRL (2007))
Anisotropic hexagonal lattice t ┴ =t/3:
in-plane mass: mxy**=4.49mxy,
out-of-plane mass: mz**=68.4/mz TBEC ≈ 300K for nb=0.1
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Resistive upper critical field of Tl2Ba2CuO6 at low temperatures and high magnetic fields
Mackenzie et al. (1993)
BCS
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V.F. Gantmakher, G.E. Tsydynzhapov, L.P. Kozeeva, and A.N. Lavrov, Zh. Eksp. Teor. Fiz. 88, 148 (1999) (also cond-mat/9903307)
Resistive transition and upper critical field in underdoped YBa2Cu3O6+x single crystals
rn > 300 m cm,
for x < 0.5
r (μ cm)
Hc2 (T)
A. Carrington, D.J.C. Walker,
A. P. Mackenzie and J. R.Cooper,
Phys. Rev. B 48, 13051 (1993)
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Upper critical field of charged
bosons:
Hc2= Ho(t-1-t1/2)3/2
ASA, ScD thesis MEPhI (1984);
Phys. Rev. B48,10571 (1993)
Upper critical field of unconventional superconductors
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Contrasting Effects of Magnetic Field on Thermodynamic and Resistive Transitions
ASA, W. H. Beere, V. V. Kabanov, and W. Y. Liang
Phys. Rev. Lett. 79, 1551 (1997)
http://prl.aps.org/abstract/PRL/v79/i8/p1551_1
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Lorenz number: evidence for 2e
prediction:
L=0.15 Le , T=0ASA and N.F. Mott,
Phys. Rev. Lett., 71, 1075
(1993)
Experimental Lorenz number in YBCO above Tc
described by the bipolaron model
theory:
K.K. Lee, ASA, and W.Y. Liang,
Phys. Rev. Lett, 90, 217001
(2003)
experiment:
Y. Zhang et al., Phys. Rev. Lett.
84, 2219 (2000)
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Normal state diamagnetism
Magnetization of charged bosons near and above Tc
(τ=T/Tc -1
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Normal state diamagnetism
Diamagnetism of optimally doped Bi-2212 (symbols: torque magnetometry by
Y. Wang, L. Li and N.P. Ong, Phys. Rev. B73, 024510 (2006))
d = ln B/lnM for B→0
ASA, Phys. Rev. Lett. 96, 147003 (2006)
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Parameter-free fit of Tc (Alexandrov & Kabanov (1999))
Tc=1.64(eRH/l4abl
2c)
1/3
LSCO (squares),
YBCZnO (circles)
YBCO (triangles)
HgBCO (diamonds)
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Isotope effect on Tc (Alexandrov (1992))
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c =By1/2exp(-T*/T) +c0
RH = RH0(1+2A2np/nb)/(1+Anp/nb)
2
r= r0[T2/T1
2+exp(-w/T)]/(1+Anp/nb)
Normal state Hall effect, resistivity and susceptibility
YBa2Cu3O7-d
ASA, V.N. Zavaritsky, S. Dzhumanov,
Phys. Rev. B 69, 052505 (2004)
y=1-exp(-Tc/T)
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La2-x SrxCuO4
GTB valence band
and impurity tails
“Waterfall” effect Real-space image of impurity
states
ARPES of impurity band tails (Alexandrov & Reynolds, PRB (2007)
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Nodal quasiparticle in pseudogapped colossal magnetoresistive manganites ,
N. Mannella, W. Yang, X. J. Zhou, H. Zheng, J. F. Mitchell, J. Zaanen, T. P. Devereaux, N. Nagaosa, Z. Hussain, Z.-X. Shen,
Nature 438, 474 - 478 (2005),
A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations
along the nodal (diagonal) and antinodal (parallel to the Cu-O bonds) directions in momentum space, generally assumed to be
linked to the "d-wave" symmetry of the superconducting state. Here we report experimental evidence that a very similar
pseudogap state with a nodal-antinodal dichotomous character exists in a system that is markedly different from a
superconductor: the ferromagnetic colossal magnetoresistive bilayer manganite La1.2Sr1.8Mn2O7. Our findings therefore cast doubt on the assumption that the nodal-antinodal dichotomy is hallmark of the superconductivity state.
Nodal-antinodal dichotomy in ARPES
)
T. Yoshida et al., Phys. Rev. Lett.
91, 027001 (2003)
La2-xSrxCuO4La1.2Sr1.8Mn2O7
http://lanl.arxiv.org/find/cond-mat/1/au:+Mannella_N/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Yang_W/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Zhou_X/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Zheng_H/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Mitchell_J/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Zaanen_J/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Devereaux_T/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Nagaosa_N/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Hussain_Z/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Shen_Z/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Shen_Z/0/1/0/all/0/1http://lanl.arxiv.org/find/cond-mat/1/au:+Shen_Z/0/1/0/all/0/1
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Single Particle Hamiltonian:
After Bogoliubov Transform:
Where ,
Bosonic Superconductor
o
BCS theory: chemical potential is within the band:
Bosonic superconductor: chemical potential is
negative and thus found outside the band.
“A.S. Alexandrov and A.F. Andreev,
Europhys Lett., 54 373 (2001)”
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ASA and J. Beanland, PRL 104, 026401 (2010)
Superconducting Gap, Normal State Pseudogap and Tunnelling Spectra
Impurity band tail
eVNS tunnelling
Energy
DOS
Charge-transfer
gap
T. Kato et al., J. Phys. Soc. Jpn. 77 (2008) 054710
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5 4 3 2 1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
Σ σ (arb. units)
0
0.2
0.4
0.6
0.8
1.0
1.2
EeV/Γ
-20 200mV
current
conductance
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Conclusions:
BCS-Migdal-Eliashberg theory breaks down at
intermediate values of the electron-phonon
coupling constant, λ≈ 0.5 (or less for strongly
correlated electrons) .
The highest Tc is reached in the crossover region
from polaronic to bipolaronic superconductivity.
In cuprate superconductors:
electron-phonon (Fröhlich) interaction is the key
pairing interaction
pseudogap is half of the bipolaron binding energy
supercarriers are (bi)polarons
disorder is essential for understanding of ARPES,
tunnelling, and normal state kinetics
ASA (1983,1988)