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

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/

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

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

Magneto-oscillations: low Fermi energy

N. Doiron-Leyraud et al., Nature 447, 565 (2007).

.

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

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).

Hubbard U and t-J “catastrophe”

J. Phys. Soc. Jpn. 76, 113708 (2007)

et al.

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

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

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

Phys. Rev. B77, 092508 (2008)

Non-adiabatic first-principle results:

Thomas Bauer and Claus Falter

Phys. Rev. B 80, 094525 (2009)

Ultrafast pump/probe determination of electron-phonon coupling

Phys. Rev. Lett (2010), in print

λ ~ 0.5 or higher (LSCO)

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

Rsc=0,1,3,∞

QMC polaron mass

(Alexandrov& Kornilovitch, PRL 1999; Spencer et al. PRB

2005)

2D,ω=0.5t

1D

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)

(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)]

Bipolaron model of cuprates (Alexandrov (1987))

Apex bipolaron (Alexandrov (1996),

Catlow et al. (1991,1998))In-plane bipolarons (ASA & Mott (1993))

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

Resistive upper critical field of Tl2Ba2CuO6 at low temperatures and high magnetic fields

Mackenzie et al. (1993)

BCS

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)

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

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

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)

Normal state diamagnetism

Magnetization of charged bosons near and above Tc

(τ=T/Tc -1

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)

Parameter-free fit of Tc (Alexandrov & Kabanov (1999))

Tc=1.64(eRH/l4abl

2c)

1/3

LSCO (squares),

YBCZnO (circles)

YBCO (triangles)

HgBCO (diamonds)

Isotope effect on Tc (Alexandrov (1992))

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)

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)

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

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)”

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

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

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)