Table Of ContentThe Gap Symmetry and
Fluctuations in High-
Superconductors
The Gap Symmetry and
Fluctuations in High-
Superconductors
Edited by
Julien Bok
Ecole Supérieure de Physique et Chimie Industrielles de Paris
Paris, France
Guy Deutscher
University of Tel Aviv
Ramat Aviv, Israel
Davor Pavuna
Ecole Polytechnique Federale de Lausanne
Lausanne, Switzerland
and
Stuart A. Wolf
Naval Research Laboratory
Washington, D.C.
KLUWER ACADEMIC PUBLISHERS
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PREFACE
Since the discovery in 1986 of high temperature superconductors by J. G. Bednorz
and K. A. Müller, a considerable progress has been made and several important scientific
problems have emerged. Within this NATO Advanced Study Institute our intention was
to focus mainly on the controversial topic of the symmetry of the superconducting gap and
given the very short coherence length, the role of fluctuations.
The Institute on ‘The Gap Symmetry and Fluctuations in High-
Superconductors’ took place in the “Institut d’Etudes Scientifiques de Cargèse” in
Corsica, France, between 1 - 13 September 1997. The 110 participantsfrom 18 countries
(yet 30 nationalities) including 23 full time lecturers, have spent two memorable weeks in
this charming Mediterranean resort.
All lecturers were asked to prepare pedagogical papers to clearly present the
central physical idea behind specific model or experiment. The better understanding of
physics of high temperature superconductivity is certainly needed to guide the
development of applications of these materials in high and weak current devices.
The chosen topics were highly controversial, so the scientific discussions were
often very lively. Even now, most controversies are not quite settled as can be seen from
the contributions in this Proceedings. Due to the considerable progress in preparation of
better quality materials we now have good single crystals hence the high precision
experiments are reproducible and reliable. Therefore it was timely to compare the results
of several recent experiments with interpretations of various theoretical models. More in-
depth research will ultimately give complete answers and thorough understanding of this
fascinating subject. At present, this volume should provide a useful insight into our
contemporary understanding of physics of high- oxides and will certainly raise a few
more profound questions. This was -indeed- the goal of this NATO Institute.
The Institute was funded by the Scientific Division of NATO in Bruxelles. We
have also benefited from a generous support of the president of the Corsican Community,
Naval Research laboratory(Washington D. C.) and the CNRS. We would like to thank all
these organizations for their support and the staff of the Cargèse Institute for their
professional help in the organization. Last but not least, we would like to acknowledge
contributions of Mme. Suzanne Beurel, who has conscientiously executed numerous
financial and secretarial tasks of this Institute.
Julien Bok, Guy Deutscher, Davor Pavuna, and Stuart Wolf
Paris, December 1997
v
INTRODUCTION
In a field still controversial despite a large amount of work, J. Bok and his co-
organizers were right, I think, to concentrate on relatively new experimental effects, on
two rather different scales: the anisotropy of superconductive gap, telling about the
microscopic pair coupling, and the thermal fluctuations neat including vortexmelting,
related to the quasi-2d structures studied. On the theoretical side, the models exposed
span the range from strong to weak electron correlations, with an unusual emphasis on the
latter.
To an ex-student of N. F. Mott since the late 40’s, these conflicts about electron
correlations seem hardly new, dating indeed as they do from the middle of the 30’s for
transition and rare earth metals and compounds
A few comments might be drawn from the background.
1. Since the parallel works of N. F. Mott and L. Landau, it has been well
understood that, in crystalline metallic conductors, the electron correlations did not spoil
the existence of electron excitations with a definite wave vector and an inverse life time
increasing from zero at the Fermi Level. The systematic observation of Fermi surfaces,
starting in the 50’s, came then as no great surprise.
What became clear much later was that, in cases such as the heavy fermions (non
magnetic) compounds, where strong correlations only affect a limited fraction of atoms,
they play less on the form of the Fermi surface than on the effective mass for excitations
from the Fermi level.
Magnetic effects are an obvious sign of electron correlations, but not necessarily
strong ones; strong correlations effects are more visible if they affect every atom involved
in conduction. Besides Mott isolation for one electron per atomic site, electron phonon
couplings leading to Kohn anomalies at 4 (instead of the usual 2 or atomic pair
couplings in Peierls singlet states are, for instance, observed in a number of 1d organic
conductors.
2. The “strong correlation” condition is bound up with the energy required for
double ionisation on an atom, compared with the independent electrons band width. This
criterion separates effectively weak correlations in transitional metals from effectively
strong correlations of the lanthanides.
What is now, in these domains, the situation in quasi-2d superconductive oxides?
Experimental Fermi surfaces and band structure studies from electron excitations seem to
point to relatively modest correlations, as in transitional metals: There is a strong analogy
with band structures as compared without correlations, and the peak of two holes
excitation is contained within the boundaries of the conduction band. One might object
that a Mott (magnetic) insulator is observed in antiferromagnetic undoped compounds.
But nothing excludes that the insulating properties below are due to an
antiferromagnetic gap of delocalised electrons and, above to scattering by magnetic
disorder (Anderson localisation). Only a very careful and extensive study of magnetic and
thermal excitations could perhaps tell the difference. This delocalised picture is also not
contradictory with the occurrence of a Peierle singlet coupling in quasi-1d ladder oxide
vii
suggests as I indeed believe, that in the oxide compounds as in the organic ones, one is
near borderlinecases.
With a band width larger than the CuO transfer energy and comparable to O and
Cu correlation energies, one can possibly treat the correlation effects as weak, with
effective intra-atomic Coulomb repulsions reduced by the S matrix effect characteristic of
repulsive interactions (roughly speaking, This is the
spirit of the treatments developed here by J. Bok and by D. Pines. However, most
theoreticians, following T. M. Rice and here M. Cyrot, take the opposite view, by using a
“tJ” modelthat neglects charge fluctuations on Cu atoms, owing to correlation repulsions
assumed much largerthan the band width.
If weak correlations apply, an approach “à la BCS” is the most natural as long as
the coherence length is definitively larger than interatomic distances, which seems to be
the case in the CuO planes; correlations from simple BCS can come from strong pair
coupling and from an anisotropy related to quasi-2 dimensionality and to the nature of
coupling.
In the standard isotropic and weak superconducting coupling BCS approach, the
details of the band structure should play a large role, as first pointed out by J. Labbé for
the A15 compounds. This has been developed by J. Bok, J. Labbé and their co-workers in
the oxides, where a strong van Hove anomaly is always present near the Fermi
level. Because it is the Lorentzian tail of the anomaly that gives the main contribution to
the van Hove peak can be somewhat away from the Fermi level or broadened by
secondary effects without decreasing very much. As the center of the peak contributes
little to it does matter that the BCS condition of fast electrons does not apply here, nor
that the effect of the peak is somewhat reduced in a strong coupling limit.
Such a BCS approach, in the weak couplinglimit, is followed by J. Bok and by D.
Pines, taking explicitly or implicitly the band structure into account, with its van Hove
anomaly. These authors differ in the microscopic nature of the pair coupling, phonons for
J. Bok and antiferromagnetic fluctuations for D. Pines. They have both considered
corrections for anisotropy, leading in both cases to anisotropicsuperconductive gaps; and
one of the purposes of this meeting was to compare experimental data with theoretical
predictions that, it must be said, do not differ very widely.
Another point of convergence/divergence refers to the AF fluctuations. Both
approaches would agree that, when they are strong, they must in quasi-2d structures,
produce a well marked magnetic pseudogap when the density of states should be lowered,
with two peaks of density of states at the edges of the pseudogap. In LaSrCu oxides, the
AF fluctuations seem to vary in period with doping as expected for a nesting condition of
the Fermi surface (indicating the importance of the band structure near the Fermi level).
The Fermi level should then fall always in the middle of the magnetic pseudogap: This
would decrease the more the AF fluctuations are marked. The maximum observed for
Tc with doping would then come, in both models, from a balance between the high due
to an approach of the van Hove anomaly and a lower due to an increase in AF
fluctuations.
In oxides such as YBaCuO, the AF fluctuations seem pinned down at the wave
length observed with no doping. The Fermi level should then shift with doping across the
psuedogap. One could even imagine that it reaches a peak of density of states bordering
the pseudogap; the effect of the pseudogap would then be to increase in that range of
doping. This is however very unlikely, as then one could not see where the stabilising
energy of the AF fluctuations would come from. AF fluctuations should indeed be more
viii
systematically studied for doping higher then the maximum of as it is difficult to
imagine a large range of doping where AF fluctuations would be weak enough to give no
appreciable pseudogap, but still strong enough to provide a sizable superconductive
coupling.
Jacques Friedel, Paris
ix
CONTENTS
INTRODUCTION
Introduction to High Temperature Superconducting Oxides 1
Davor Pavuna
Status of 15
Guy Deutscher
THEORIES AND MODELS
Superconductivity in Cuprates, The van Hove Scenario: A Review 37
Julien Bok and Jacqueline Bouvier
The Isotope Effect and Pair Breaking in Cuprate Superconductors 55
Vladmir Z. Kresin, Andreas Bill, Stuart A. Wolf, and Yuri N. Ovchinnikov
Mott Metal-Insulator Transition in Oxides 73
Michel Cyrot
Scaling Behavior of the Normal State and Superfluid Density in Metallic 91
Cuprates
Victor V. Moshchalkov, Bart Wuyts, Annemie Steegmans, Rick Provoost,
Roger E. Silverans, and YuanBruynseraede
The Nearly Antiferromagnetic Fermi Liquid Model 111
David Pines
The Marginal Fermi Liquid Model 143
Chandra Varma
MATERIALS AND APPLICATIONS
Current Research Issues for the Electron-Doped Cuprates 145
Patrick Fournier, E. Maiser, and Rick L. Greene
Superconductivity of Heavy-Electron Compounds: Comparison with 159
Cuprates
Hans-Rudolf Ott
The Inhomogeneity of Superconductors 171
Zhong-Xian Zhao and X. L. Dong
xi
Applications of HTS in Space and Electronics 185
Stuart A. Wolf
OPTICAL SPECTROSCOPIES
Photoemisson as a Probe of Superconductivity 195
Giorgio Margaritondo
Electronic Structure and Doping in Cuprate Superconductors 209
Marshall Onellion
Electronic Structure of High-Tc SuperconductorsObtained by Angle 229
Resolved Photoemission
Juan-CarlosCampuzano, Mohit Randeria, Michael Norman, and Hong Ding
Light Scattering from Charge and Spin Excitations in Cuprate Systems 249
Rudi Hacki
Topological Analysis of the Superconducting Gap by Electronic Raman 291
Scattering in Hg-1223 Single Crystals
Alain Sacuto and Roland Combescot
MAGNETIC PROPERTIES
Evidence for Gap Asymmetry and Spin Fluctuations from Nuclear 309
Magnetic Resonance
Steffen Kraemer and Michael Mehring
NMR in the Normal State of Cuprates 331
Arlette Trokiner
From Magnons to the Resonance Peak: Spin Dynamics in 349
Superconducting Cuprates by Inelastic Neutron Scattering Experiments
Philippe Bourges
THERMODYNAMIC PROPERTIES AND FLUCTUATIONS
MagneticPenetration Depths in Cuprates: A Short Review of 373
Measurement Techniques and Results
Walter N. Hardy, Saeid Kamal, and D. A. Bonn
Specific Heat Experiments in High Magnetic Fields: d-Wave Symmetry, 403
Fluctuations,Vortex Melting
Alain Junod, MarlyseRoulin, Bernard Revaz, Andreas Erb, and Eric Walker
The Spectrum of Thermodynamic Fluctuations in Short Coherence 423
Length Superconductors
Andrea Gauzzi
Multilayering Effects on the Thermal Fluctuations of Cooper Pairs 443
around the Superconducting Transition in Cuprates
Felix Vidal and Manuel V. Ramallo
xii
C-Axis Conductivity and the Role of d-Wave Superconductivity and 465
Fluctuations on Anisotropic High Temperature Superconductors
Colin E. Gough
TUNNELING EXPERIMENTS
ScanningTunneling Microscopy on High Temperature Superconductors 487
Oystein Fischer, Christian Renner, and Maggio Aprile
Flux Quantization Experiments in Cuprate Superconductors 503
John R. Kirtley, C. C. Tsuei, and K. A. Moler
Tunneling In High-Tc Superconduction Cuprates 511
Jerome Lesueur, Brigite Leridon, Marco Aprili, and Xavier Grison
From the Andreev Reflection to the Shavin Contact Conductance 537
Guy Deutscher and Roger Maynard
CONCLUDING REMARKS 557
Julien Bok
Index 559
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