Percolation, Localization, and Superconductivity

468 Pages·1984·12.61 MB·English

by  Stuart A. Wolf (eds.)

Percolation,
Localization, and
Su percond uctivity
NATO ASI Series
Advanced Science Institutes Series
A series presenting the results of activities sponsored by the NA TO Science Committee,
which aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
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Recent Volumes in this Series
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Volume 10B-Polarons and Excitons in Polar Semiconductors and
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edited by J. T. Devreese and F. Peeters
Volume 10g-Percolation, Localization, and Superconductivity
edited by Allen M. Goldman and Stuart A. Wolf
Series B: Physics
Percolation,
Localization, and
Superconductivity
Edited by
Allen M. Goldman
School of Physics and Astronomy
University of Minnesota
Minneapolis, Minnesota
and
Stuart A. Wolf
Metal Physics Branch
Naval Research Laboratory
Washington,D.C.
Plenum Press
New York and London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on
Percolation, Localization, and Superconductivity,
held June 19-July 1, 1983,
at Les Arcs, Savoie, France
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute on Percolation, Localization, and Superconduc-
tivity (1983: Savoie, France)
Percolation, localization, and superconductivity.
(NATO ASI series. Series B, Physics; v. 109)
"Proceedings of the NATO Advanced Study Institute on Percolation, Localiza-
tion, and Superconductivity, held June 19-July 1, 1983, at Les Arcs, Savoie,
France."
Bibliography: p.
Includes index.
1. Solid state physics-Congresses. 2. Superconductivity-Congresses. 3. Per-
colation (Statistical physics)-Congresses. I. Goldman, Allen M. II. Wolf, Stuart
A. III. Title. IV. Title: Localization, and superconductivity. V. Series: NATO ad-
vanced science institute series. Series B, Physics; v. 109.
QC176.A1N326 1983 530.4'1 84-8357
ISBN-13: 978-1-4615-9396-6 e-ISBN-13: 978-1-4615-9394-2
DOl: 10.1007/978-1-4615-9394-2
Copyright is not claimed for those portions of this book resulting
from work performed as part of U.S. government employees' duties.
© 1984 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1984
A Division of Plenum Publishing Corporation
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All rights reserved. No part of this book may be reproduced, stored in a retrieval system,
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PREFACE
The study of the effects of dimensional ity and disorder on
phase transitions, electronic transport, and superconductivity has
become an important field of research in condensed matter physics.
These effects are both classical and quantum mechanical in nature
and are observed universally in urealu materials. What may at
first glance seem a diverse collection of lectures which form the
chapters of these proceedings is in fact, an attempt to demon-
strate the commonality, inter-relationship, and general applica-
bility of the phenomena of localization, percolation, and macro-
scopic quantum effects on electrical transport and superconduc-
tivity in disordered solids. The theory of these phenomena is
presented in a complete, yet, self-contained fashion and the
inter-relationship between the topics is emphasized. An extensive
treatment of experimental results is also included, both those
which have stimulated the theory as well as those that have
confirmed it.
Many of the phenomena investigated in this field also have
technological significance. For example, the nature of electronic
localization in metals in which one or more dimensions are con-
strained is very important when one attempts to predict the be-
havior of the metallic interconnects in ultra-miniature circuits.
The macroscopic quantum tunneling phenomenon which is closely
associ ated with the concept of quantum noi se may determi ne the
ultimate sensitivity of Josephson devices to electromagnetic
signals. Granular superconductors and arrays of Josephson de-
vices which are studied here in the context of statistical mechan-
ics and phase transitions may serve as generators or detectors of
high-frequency electromagnetic radiation. A clear understanding
of the nature of the metal-insulator or the superconductor-
insulator transitions in random percolating systems may be import-
ant in the technological exploitation of the anomalous behavior
at these critical points. Furthermore, the fabrication techni-
ques used and in some instances developed in these contexts are
currently applicable to digital superconducting electronics.
v
vi PREFACE
This book is based on lectures given at the NATO ASI entitled
"Percolation, Localization, and Superconductivity" held from June
19th to July 1st, 1983 at Les Arcs in Savoie France. We have
attempted to organize it in a generally coherent fashion, using
one topic to build on the next. The topics are sufficiently
well-established allowing for a pedalogical treatment, but cer-
tainly the "state-of-the-art" is rapidly evolving.
An important feature of the book are the chapters which
present the current state of development of what M. Tinkham in his
summary of the Institute called our "High-Tech Industrial Civili-
zation". These review the fabrication techniques that have
become available partly because of the semiconductor industry and
the need for ultra-small digital circuitry. The remainder of the
book is devoted to a series of experimental and theoretical topics
in condensed matter physics relating to electronic transport and
superconductivity in disordered and dimensionally constrained
materi al s.
The book proceeds from macroscopic quantum tunneling (MQT) to
small particles, percolation, localization, two-dimensional super-
conductivity, commensurate and incommensurate phases of a two-
dimensional vortex lattice, and finally granular superconductivity.
The study of MQT is the newest subject in this grouping and
is of fundamental significance for the quantum theory of measure-
ment. Josephson junctions or Superconducting Quantum Interference
Devices (SQUIDs) are ideal model systems for work in this field.
Low temperatures are needed to suppress thermal activated proces-
ses. A complete understanding of the role of damping in these
systems appears to require more experimental and theoretical
work.
In the study of percolation in real superconducting systems
experiments show a remarkable semiquantitative agreement with
simple model predictions. Advances in the characterization of
sample geometries should result in even more quantitative compar-
ison of experiment and theory in the future.
The theory of weak localization bears a remarkable resemblance
to the theory of superconductivity. It seems to describe experi-
ments extremely well. The strong localization regime is not yet
served by an elegant formal theory combining all effects.
Two-dimensional superconducting systems such as amorphous and
granular thin films and weakly-coupled arrays appear to provide
excellent model systems for the investigation of both the con-
tinuum and discrete realizations of the Kosterlitz-Thouless
transition. Measurements of electrical resistance vs temperature
above the transition yield the temperature-dependent free vortex
PREFACE vii
density. Studies of the nonlinear voltage-current characteristic
and the kinetic inductance yield the temperature-dependent super-
electron density. Additional experiments, in which various
parameters of the theory are determined independently, are needed
to furth~r clarify the issues in this area.
The study of granular superconductors and composites of small
particles is a relatively old subject. It involves the under-
standing of systems of isolated grains as well as coupled systems.
It is important in the context of the other subjects of this
Institute because randomness, percolation, localization, and
quantum tunnel i ng are theoretical concepts recogni zed as bei ng
relevant to the understanding of granular materials.
Our intent in organizing an Advanced Study Institute was to
make evident the opportunities in this field. We hope that the
reader of these proceedings will agree with us that that field
is a fertile area of research.
Allen M. Goldman and Stuart A. Wolf
ACKNOWLEDGEMENTS
This AS! was organized on a rather short time scale and many
individuals made important contributions to its ultimate success.
Dr. R. Sinclair of the NATO Advanced Study Institutes Programme
deserves special thanks for his patience in dealing with the neo-
phyte organizers. A significant financial contribution to the
travel of participants from the USA was made by the NSF-Low
Temperature Physics Program under Grant NSF/DMR-8302327. S. Fo~er,
K. Gray, and J. Ruvalds were very helpful in sharing with us their
previous experience in organizing NATO ASI's. Bernard Croise and
Philipe Fabing of the Les Arcs resort deserve special thanks for
their efforts on behalf of the Institute. John Cl aassen, Tom
Francavilla, Wendy Fuller, Don Gubser, Deborah Van Vechten, and
Beverly Wood made important contributions to a number of activ-
ities including the preparation of these proceedings. Kay Reilly
and Ina Rubenstein helped with financial and travel arrangements,
respectively. The Naval Research Laboratry and the School of
Physics and Astronomy of the University of Minnesota contributed
materi ally to the preparation of these proceedi ngs and to the
organizational effort for the AS!. The organizers especially
acknowledge the rather substantial efforts of their secretaries,
Evelyn Backman of the University of Minnesota and Lahni Blohm of
the Naval Research Laboratory, in making the Conference and these
proceedings a success.
ix
CONTENTS
Macroscopic Quantum Tunneling and Related Effects in
Josephson Systems......................................... 1
A.J. Leggett .
Quantum Dynamics of Superconductors and Tunneling Between
Supcond uctors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Vinay Ambegoakar
Small Particles........................................... 65
B. MUhlschlegel
Partially Connected Systems............................... 83
P.G. de Gennes
Perco 1a t i on and Superconduct i vi ty. . . . . . . . . . . . . . . . . . . . . . . . . 95
Guy Deutscher
Art i fi cia 11 y-Structured Superconductors................... 115
M.R. Beasley
Clustering in Thin Au Films Near the Percolation
Thresho 1d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
R.B. Laibowitz, R.F. Voss, and E.I. Alessandrini
Theory of the Weakly Localized Regime.... ................. 161
Hidetoshi Fukuyama
Loca 1i zt i on and Supercond uct i vity. . . . . . . . . . . . . . . . . . . . . . . . . 189
Yoseph Imry
Microfabrication Techniques for Studies of Percolation,
Localization, and Superconductivity and Recent
Experimental Results...................................... 231
Daniel E. Prober
xi
xii CONTENTS
Fabrication of Sub -0.1 ~m Fine Metal Lines Using High
Resolution Electron Beam Techniques with Contamination
Resist.................................................... 267
R.B. Laibowitz and C.P. Umbach
Two-Dimensional Coulomb Gas and Connection to
Superconducting Films ......................... ~........... 287
Peter Minnhagen
Two-Dimensional Transition Superconducting Films.......... 325
J. E. Mooi j
Static and Dynamic Properties of Commensurate and
Incommensurate Phases of a Two-Dimensional Lattice of
Superconducting Vortices.................................. 371
P. Martinoli, H. Beck, M. Nsabimana, and G.A. Racine
Pinning by Ordinary Defects in Ordinary Superconductors... 395
Dierk Rainer
Granular Superconductors and Josephson Junction Arrays.... 401
S. Doniach
Disorder in Weakly Coupled Granular Superconductors....... 431
J. Rosenb 1a tt
PARTICIPANTS.............................................. 453
INDEX..................................................... 459