Gulian A.M., Zharkov G.F. Nonequilibrium Electrons and Phonons in Superconductors
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Nonequilibrium
Electrons and Phonons
in Superconductors
SELECTED TOPICS IN SUPERCONDUCTIVITY
Series Editor: Stuart Wolf
Naval Research Laboratory
Washington, D. C.
CASE STUDIES IN SUPERCONDUCTING MAGNETS: DESIGN AND OPERATIONAL ISSUES
Yukikasu Iwasa
ELECTROMAGNETIC ABSORPTION IN THE COOPER OXIDE SUPERCONDUCTORS
Frank J. Owens and Charles P. Poole, Jr.
INTRODUCTION TO HIGH-TEMPERATURE SUPERCONDUCTIVITY
Thomas Sheahen
THE NEW SUPERCONDUCTORS
Frank J. Owens and Charles S. Poole
NONEQUILIBRIUM ELECTRONS AND PHONONS IN SUPERCONDUCTORS
Armen M. Gulian and Gely F. Zharkov
QUANTUM STATISTICAL THEORY OF SUPERCONDUCTIVITY
Shigeji Fujita and Salvador Godoy
STABILITY OF SUPERCONDUCTORS
Lawrence Dresner
A Continuation Plan is available for this series. A continuation order will bring delivery of each new volume immediately
upon publication Volumes are billed only upon actual shipment. For further information please contact the publisher.
Nonequilibrium
Electrons and Phonons
in Superconductors
Selected Topics in Superconductivity
Armen M. Gulian
USRA / Naval Research Laboratory, Washington, D. C. 20375, USA
and
Gely F. Zharkov
P. N. Lebedev Physics Institute, Moscow 117333, Russia
KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: 0-306-47087-X
Print ISBN: 0-306-46075-0
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Foreword
Superconductivity occupies a special, unique place in the 20
th
century physics. Just
think of it: its microscopic mechanism was understood only in 1957—46 years after
the discovery of superconductivity in 1911. In contrast, the theory of normal metals
behavior (or, to be more precise, the theory of metals in normal state) was formed
as early as the twenties, immediately following the creation of quantum mechanics.
Moreover, when I took up the theory of superconductivity in 1943, not only
microscopic theory was non-existent, but even macroscopic superconductivity
theory was quite incomplete. The problem is that the Londons equations, introduced
in 1935, allow only a quantitative description of superconductors in magnetic fields
weak in comparison with the critical field. Also, even in weak fields, the Londons
theory is strictly applicable only to Type-II superconductors—although the division
of superconductors into Type-I and Type-II materials was not suggested until much
later, in early 1950’s. As far as nonequilibrium phenomena are concerned, then until
1943 the most remarkable, yet proved to be fault afterwards, implication was that
of a complete absence of all thermoelectric effects in superconducting state.
Look how radically the picture has changed in only 55 years! Perhaps for
younger generation this would seem a whole lot of time. Is it? Indeed, it is just an
average human life-span. And if the same pace is maintained then what will we
have 55 years later, in 2053? I am not capable of an extrapolation of this magnitude,
without risking being caught in the act of daydreaming. I could only assume that
the development would take two major directions.
The first direction—exploration of high temperature superconductors. Clearly,
their application in technology, the possibilities of which were vastly overestimated
when they were initially discovered 10 years ago, will sharply increase in this
period. There can hardly be any doubt that a microtheory of superconducting
cuprates, still lacking, will be fully understood by then. The most interesting yet,
are trials aimed at raising critical temperature to create room-temperature super-
conductors. There is no recipe for success here. However, the existing theoretical
grounds, do not contradict this possibility in any way. The situation here reminds
v
vi FOREWORD
the one with the high-temperature superconductivity between 1964, when this
problem had received exposure, and 1986–1987, when it got its well-known
solution. I remember very well the grinning faces of those skeptics who would ask
me sarcastically, “Whatever happened to your heat-resistant superconductivity?” It
is quite possible that as far as the room-temperature superconductivity goes, the
skeptics would this time prove to be right. Still, it is imperative to keep searching
for that kind of superconductivity, and I for one, believe in it.
The second avenue of development that I mentioned above, is nonequilibrium
superconductivity. Even for “usual” or, more specifically, isotropic and weakly
anisotropic superconductors, much less has been done in this area than for super-
conductors in equilibrium. It is especially vivid in the case of thermoelectric effects.
Despite the faultiness of the statement of complete absence of all thermoelectric
effects in superconducting state was clarified as early as in 1944, it was ignored for
many years, and even today the picture is still not very clear. The reader will learn
about it in Chapters 13–14 of this book. We have many questions here, both in
theory and experiment. I am inclined to think that they will find the answers in near
future. This is only right in case of “ordinary” superconductors. As far as strongly
anisotropic high temperature superconductors and
“
unconventional
”
ones in gen-
eral are concerned, the satisfying theory of nonequilibrium phenomena for them
has not been developed. The authors of this book point out that only isotropic
superconductors are discussed. It is obviously a forced limitation. Besides, even in
case of nonequilibrium processes in isotropic superconductors there is plenty of
material, which is presented in the book. Other contemporary monographs, to the
best of my knowledge, do not exist.
In the light of the aforementioned there is little doubt that the monograph by
A. M. Gulian and G. F. Zharkov is actual and desired. I have to admit that I would
like to have seen the book more physics-minded, less formal, more transparent and
more accessible to a wider physicist audience. Though, and it is a common
knowledge, “better is the enemy of good.” The authors have done an enormous
amount of work to the benefit of the physical community at large, and I believe the
book will provide a stimulus for further experimental and theoretical investigations.
V. L. Ginzburg
Moscow, 1998
Preface
“
I wanted most to give you some appreciation of the wonderful world and the
physicist’s way of looking at it, which, I believe, is a major part of the true cul-
ture of modern times.
”
Feynman’s Epilogue
(Courtesy of Addison-Wesley)
The appearance of any new book raises several questions. What contents are
included under the title? What benefit can I get out of here? What motivated the
authors to write this book?
It is about nonequilibrium superconductivity. Typically, articles are written for
the professionals in a field, while books serve a wider audience. In part they seek
to share the excitement of the work, to attract more individuals to the field, and
thereby create more professionals.
So how do we explain the essence of “nonequilibrium superconductivity” to
the potential readers of this book? The following discussion has always been helpful
even for the people far from superconductivity. Human beings themselves are a
system containing large number of atoms in a nonequilibrium state. The equilibrium
state of such a system is a plain mixture of atoms. It is the nonequilibrium state that
reveals all the wonders of life! The same large qualitative difference exists between
superconductivity in thermodynamic equilibrium and in its nonequilibrium state.
What ideas unify the content of this book? Superconductors are inherently
quantum mechanical object despite their macroscopic physical scale. The micro-
scopic theory of superconductivity generated by Bardeen, Cooper, and Schrieffer
provided a firm basis for the -theory of superconductivity, earlier postulated by
Ginzburg and Landau. Further generalization of the theory provide a method of
dealing the time-dependent problem, the TDGL-equations. Chapter 2 reviews the
development of the arguments that TDGL-equations strictly apply only in the case
of gapless superconductors—an old statement, which is wrong nowadays: after
passing through Chapters 3-6 the readers will recognize in Chapter 7 that there is
vii
viii
PREFACE
a modified TDGL scheme which is unequivocally valid for the much more general
case of finite-gap materials! This derivation combines the very general equations
applicable to equilibrium (Chapter 1) and nonequilibrium (Chapter 3) supercon-
ductivity. Both the Keldysh and Eliashberg-Gor’kov analytical continuations tech-
nique are exploited to prove the same results are achieved.
It is really amazing how nicely these two mathematically very different tools
yield precisely the same results! Given this equivalence of the results, the reader
might wonder which is preferable from a practical point of view. We conclude that
for the phenomena which have already been treated in equilibrium in the Matsubara
technique it is faster to apply the analytical continuation method. In general,
Keldysh’s method is more straightforward.
Since nonequilibrium superconductivity exploits some concepts which do not
occur in equilibrium case, such as the longitudinal electric field penetration depth
and branch imbalance potential, we devoted a special discussion (Chapter 8) to
collective oscillations. These are formally out of the range of applicability of TDGL.
The kinetic equations, which follow from the general nonequilibrium equations
(Chapter 4), provided the mathematical basis to discuss various nonequilibrium
effects in superconductors. We tried everywhere to treat nonequilibrium electrons
and phonons on an equal footing. Thus in parallel to enhancement of the order
parameter (Chapter 5), we considered the accompanying phonon deficit effect
(Chapter 6). In this two chapters the collision integrals, which traditionally serve
to describe the relaxation processes, were used also to describe the sources of
nonequilibrium deviation of both electrons and phonons.
The behavior of nonequilibrium Josephson junctions and the more novel but
closely related phase-slip centers are treated in detail in Chapters 10 and 9
respectively. Attention is paid to both the phonon and electron components.
Irradiation by lasers is a traditional method for creating a nonequilibrium
superconducting state (see Chapter 11). In Chapter 12 we considered the inverse
problem: the ability of a superconductor in a nonequilibrium state to act as a
coherent phonon or photon generator. This laser-like source behaviors have not yet
been experimentally confirmed. However, we hoped our discussion will encourage
their demonstration.
The final chapters of the book, 13 and 14, discuss thermoelectricity. This topic
is one of the most complex, subtle featured and thus intellectually captivating in
solid state physics. The addition of superconductivity to the discussion creates even
more opportunity to be excited by thermoelectricity.
The book's initial chapter includes an introduction to the theory of supercon-
ductivity for those readers not already acquainted with it. The treatment is very
concise but covers the most important physical concepts which will later be
assumed to be familiar to the reader. The mathematical constructs of quantum field
theory are assumed to need no explanation.
PREFACE ix
We should apologize for all the possible drawbacks the book may have and
encourage any reader's response. We have restricted ourselves to discussions of the
phenomena mainly in conventional, low temperature superconductors. This is less
a disadvantage than one might assume since our book is focused exclusively on the
theory. Experimental facts referred to only for some illustrative purposes. Hope-
fully, in the third millennium the mechanism of equilibrium phenomenon in
high-temperature superconductors will be completely understood, and many new
nonequilibrium phenomena and their theoretical explanations will enlarge super-
conductivity. To assist this process we have written this book. Actually, while an
apology may be due for the purely theoretical focus, we note the ancients’ belief
that “nothing is more practical than a good theory.”
In general, studying nonequilibrium phenomena, we feel ourselves to be
climbing onto the “shoulders of giants.” We now invite the readers to come enjoy
with us what we have seen of nonequilibrium superconductivity from this elevated
perch. If the readers can see more than we did, we will consider our tasks fulfilled.
Finally, we would like to use this opportunity to acknowledge numerous
fruitful discussions with our teachers, students, colleagues, and friends—these
discussions assisted greatly to the appearance of this book in its present form.
Armen M. Gulian
Gely F. Zharkov
Washington, D. C., USA - Moscow, Russia
1998