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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. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical D. Reidel Publishing Company and Physical Sciences Fordrecht Boston, and Lancaster D Behavioral and Social Sciences Martinus Nijhoff Publishers E Engineering and The Hague, Boston, and Lancaster Materials Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, and Tokyo Recent Volumes in this Series Volume 103-Fundamental Processes in Energetic Atomic Collisions edited by H. O. Lutz, J. S. Briggs, and H. Kleinpoppen Volume 1D4-Short-Distance Phenomena in Nuclear Physics edited by David H. Boal and Richard M. Woloshyn Volume 105-Laser Applications in Chemistry edited by K. l. Kompa and J. Wanner Volume 106-Multicritical Phenomena edited by R. Pynn and A. Skjeltorp Volume 107-Positron Scattering in Gases edited by John W. Humberston and M. R. C. McDowell Volume 10B-Polarons and Excitons in Polar Semiconductors and Ionic Crystals 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 233 Spring Straet, New York, N.Y. 10013 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 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
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