Pair Correlations in Many-Fermion Systems

290 Pages·1998·19.826 MB·English

by  Lev P. Gor’kov (auth.), Vladimir Z. Kresin (eds.)

Pair Correlations in
Many-Fermion Systems
Pair Correlations in
Many-Fermion Systems
Edited by
Vladimir Z. Kresin
Lawrence Berkeley Laboratory
University of California
Berkeley, California
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
On file
Proceedings of an Advanced Study Institute School on Pair Correlations in
Many-Fermion Systems, held June 5-15,1997, in Erice, Sicily, Italy
ISBN 978-1-4899-1557-3 ISBN 978-1-4899-1555-9 (eBook)
DOI 10.1007/978-1-4899-1555-9
© 1998 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1998
Softcover reprint of the hardcover 1st edition 1998
10987654321
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form
or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise,
without written permission from the Publisher
PREFACE
At first glance, the articles in this book may appear to have nothing in common. They
cover such seemingly disparate subjects as the properties of small metallic clusters and the
behavior of superfluid He3, nuclear physics and organic materials, copper oxides and mag
netic resonance. Why have they been brought together, particUlarly in our time of narrow spe
cialization?
In fact, the properties and effects described in this book touch upon one and the same
fundamental phenomenon: pair correlation. Introduced in the theory ofs uperconductivity by
J. Bardeen, L. Cooper, and J. Schrieffer (BCS), this effect plays a key role in various Fermi
systems.
The book consists of several sections. The first chapter is concerned with conven
tional and high Tc superconductors. The second chapter describes two relatively young fami
lies of superconductors: organics and fullerenes. Chapter III addresses the superfluidity of
He3• The discovery of this phenomenon in 1971 was a big event in physics and last year was
acknowledged by a Nobel prize. This book contains the text oft he Nobel lecture. Chapters IV
and V are devoted to correlations in finite Fermi systems such as small metallic clusters, C
60
anions, and atomic nuclei.
The book thus covers a broad range of problems, illuminating the close ties between
various areas of physics.
Almost all of the included papers were presented as Lectures at the International
School on Pair Correlation in Many-Fermion Systems (Erice, Sicily, June 1997). The idea of
the School was to bring together leading scientists working in different fields and demon
strate to the students (and now to the readers) the mutual influence ofv arious branches of sci
ence. This multidisciplinary scenario found a welcoming home at the superb Majorana
Scientific Centre in Erice.
I would like to express special thanks to Prof. G. Benedek (University di Milane), Di
rector of the School of Solid State Physics, and to Prof. A. Bussman-Holder (Max-Planck In
stitut, Stuttgart) for their help in organizing the School.
I am also grateful to A. Bill and to E. Dynin for their help in the preparation of this
book.
Vladimir Z. Kresin
v
CONTENTS
I. Superconducting State in Conventional and High Tc Oxides
Foundations of Superconductivy and Extension to Less-Common Systems 3
L. Gor'kov
The Isotope Effect in Superconductors ...................................... 25
A. Bill, V. Z. Kresin, and S. Wolf
Hyperfine Interactions in Metals ........................................... 57
W. D. Knight
Perovskite Oxides: A Rick.and Fascinating Crystal Class Family . . . . . . . . . . . . . . . .. 63
A. Bussmann-Holder
Josephson Effect: Low-Tc vs. High-Tc Superconductors. . . . . . . . . . . . . . . . . . . . . . .. 75
A. Barone
The Spectrum of Thermodynamic Fluctuations in Short Coherence Length
Superconductors ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89
A. Gauzzi
Microwave Response of High-Tc Superconductors ............................ 111
A. Ag1iolo Gallitto, I. Ciccarello, M. Guccione, and M. Li Vigni,
D. Persano Adorno
II. Organic Superconductivity. Fullerenes
Structure and Phase Diagram of Organic Superconductors ...................... 135
T. Ishiguro and H. Ito
Pairing and Its Mechanism in Organic Superconductors ........................ 147
T.lshiguro
Superconductivity in Doped C Compounds ................................. 155
60
O. Gunnarsson, E. Koch, and R. Martin
On the Pair Correlations between Electrosolitions ............................. 173
L. Brizhik and A. Eremko
vii
III. Superfluid He3
The Pomeranchuk Effect 187
R. Richardson
Pair Correlations in Superfluid Helium 3 .................................... 205
D. Vollhardt
IV. Finite Systems. Clusters
Non-Adiabacity and Pairing in the Finite Systems ............................. 223
V. Z. Kresin
Fullerene Anions and Pairing in Finite Systems ............................... 235
Th. Jolicoeur
Quantized Electronic States in Metal Microclusters: Electronic Shells, Structural
Effects, and Correlations ............................................. 245
V. V. Kresin and W. Knight
V. Finite Systems. Nuclei
Role of Pairing Correlations in Cluster Decay Processes ........................ 265
D. S. Delion, A. Insolia, and R. J. Liotta
Index ................................................................. 295
viii
I. SUPERCONDUCTING STATE
IN CONVENTIONAL AND HIGH Tc OXIDES.
FOUNDATIONS OF SUPERCONDUCTIVITY
AND EXTENSION TO LESS-COMMON SYSTEMS
Lev P. Gor'kovl.2
lNational High Magnetic Field Laboratory, Florida State University
2L.D.Landau Institute for Theoretical Physics
Russian Academy of Sciences
Abstract
The review of fundamentals of the microscopic theory of superconductivity, as
a whole, serves to the purpose to elicit a knowledge about theoretical results and
qualitative statements which would be robust enough to allow a judgment regarding
the nature of superconductivity in such uncommon superconductors, as cuprates or
superconductors of the Heavy Fermion family.
INTRODUCTION
Phenomenon of superconductivity long ago is an integral part of our education
and our everyday life. It is especially so now, after the discovery by Bednorz and
Muller of the so-called "High Temperature Superconductivity" in cuprates, for which
critical temperatures, Te's, amount to the range of '" lOOK, far exceeding the nitrogen's
liquefaction temperature (of 77K).
Needless to say, we are now witnessing enormous experimental and theoretical
struggle in attempts to explain unusual cuprates' properties and disclose the mecha
nism for so high a transition temperature. However, whenever superconductivity itself
is discussed, even in cuprates more often than not, one applies views and concepts
borrowed from the experience accumulated in about four-decades-Iong studies of more
"common" (low Tc) superconductors. During that time a few scientific generations have
changed, and, as today, it seems very timely to outline the basic concepts and methods
by which superconductivity can be approached.
In the classical Bardeen, Cooper, and Schrieffer's (BCS) theoryl of superconduc
tivity, one is to distinguish between its two main constitutions: the phonon-mediated
attraction between electrons, as a mechanism for superconductivity, and possibility of
the Fermi liquid's instability caused by a weak interaction, commonly known as the
"Cooper phenomenon". This latter one has proved to be of a broader significance,
while giving rise to more or less straightforward generalization of the original BCS the
oretical scheme. The well-known realization of the views are properties of superfluid
3
3He, superconductivity in the so-called "Heavy Fermions" (HF) materials and, possibly,
superconductivity in high-Tc cuprates.
In what follows we outline the main results of the theory of superconductivity by
adopting the view that transition into superconducting state, as induced by a Cooper
instability2, is phase transition: it changes the electrons' symmetry and, hence, must
be characterized by an order parameter3. Starting with discussion of the Cooper insta
bility, we develop symmetry approach to superconductivity. Competing interactions,
weak coupling limit VB. strong coupling (in the frameworks of the phonon model) etc.,
are also topics of our interest. The model is then generalized to anisotropic metals
and arbitrary shape of the Fermi surface, with a more extended discussion of broken
symmetries of the superconducting order parameter. The effects of impurities are also
considered in some detail. At the end we briefly summarize our review and comment
on the current situation in superconducting cuprates.
The discussion, as a whole, serves to the purpose to elicit a knowledge about the
oretical results and qualitative statements which would be robust enough to allow a
judgment regarding the nature of superconductivity in such uncommon superconduc
tors, as cuprates or superconductors of the Heavy Fermion family.
Throughout the text the basic knowledge of diagrammatic methods (Green func
tions, Feynman diagrams, etc.) is supposed.4,5
COOPER'S INSTABILITY
Although the original paper by Cooper2 was based on an oversimplified model and
some unjustified assumptions, its conclusions, nevertheless, have removed the main
hurdle on the way to understanding the phenomenon of superconductivity. Namely,
although superconductivity was known to be a widespread property of metals, it ap
peared to be a low temperature phenomenon, as characterized by critical temperatures
in the range of I + 10K for common superconductors -an energy scale exceedingly small
compared with typical electronic energies ('" leV), or even with characteristic phonon
frequencies, w '" 102K . (The lattice's participation in the phenomenon has been known
since the discovery of the isotope effect in 19506). Smallness of Tc, hence, would have
implied a weakness of the effective interactions, while the quantum mechanics teaches us
that for the three-dimensional processes even attractive but arbitrary weak interactions
would produce no singularities. According to 2, the situation drastically changes for
electrons in the presence of the Fermi sea. A more rigorous proof sketched below, shows
that the normal ground state of a metal may become unstable when e-e-interactions
are taken into account (see 4 for more details).
Let u(p~ -P1) be the Fourier component of some short range interaction, U(r-r'),
between electrons (shown in Figure la as the dashed line), which gives rise to the
matrix element for scattering of two electrons, (0"1, P1) and (0"2, Pz), with the momentum
transfer (p~ - P1). Consider now the perturbation series in the form of the ladder
diagrams of Figure 1b , which may be summed up by writing it as the diagrammatic
equation for the vertex r <7=,_<7 ;<7' ,-c·I (p, q - Pi p', q - p') in Figure Ic. (Here we use the
4-dimensional notations, p (p,w), where w is the discrete thermodynamic frequency,
w == iWni W. . = (2n + 1) 7I"T for the fermionic lines). The kernel of this integral equation,
according to Figure 1b , is given by
-TEj
u(p - p) Q(p)Q(q _ p)d3p (1)
e (271")3
where Q(P) are the thermodynamic Green functions of free electrons:
_ 1
Q(p) :; ie" - e(p) + I' (2)
=
The reason for selecting the ladder diagrams ill Figure Ib becomes clear if q 0 (or
is small). Two electronic states (O",p) and (-0", -p) are then related to each other by
4