Localization, Interaction, and Transport Phenomena: Proceedings of the International Conference, August 23–28, 1984 Braunschweig, Fed. Rep. of Germany PDF
Preview Localization, Interaction, and Transport Phenomena: Proceedings of the International Conference, August 23–28, 1984 Braunschweig, Fed. Rep. of Germany
61 Springer Series in Solid-State Sciences Edited by Peter Fulde Springer Series in Solid-State Sciences Editors: M. Cardona P. Fulde H.-J. Queisser 40 Semiconductor Physics 51 Phonon Scattering in Condensed Matter An Introduction By K Seeger Editors: W. Eisenmenger, K LaBmann, 41 The LMTO Method and S. D6ttinger Muffin-Tin Orbitals and Electronic 52 Superconductivity in Magnetic and Exotic Structure Materials By H. L. Skriver Editors: T. Matsubara and A. Kotani 42 Crystal Optics with Spatial Dispersion, 53 Two-Dimensional Systems, and Excitons Heterostructures, and Superlattices By V. M. Agranovich and V. L. Ginzburg Editors: G. Bauer, R Kuchar, 43 Resonant Nonlinear Interactions of and H. Heinrich Light with Matter 54 Magnetic Excitations and Fluctuations By V. S. Butylkin, A. E. Kaplan, Editors: S. Lovesey, U. Balucani, R Borsa, Yu. G. Khronopulo, and E. 1. Yakubovich and V. Tognetti 44 Elastic Media with Microstructure II Three-Dimensional Models 55 The Theory of Magnetism II. By 1. A. Kunin Thermodynamics and Statistical Mechanics By D. C. Mattis 45 Electronic Properties of Doped Semiconductors 56 Spin Fluctuations in Itinerant Electron By B. I. Shklovskii and A. L. Efros Magnetism By T. Moriya 46 Topological Disorder in Condensed Matter 57 Polycrystalline Semiconductors, Editors: R Yonezawa and T. Ninomiya Physical Properties and Applications 47 Statics and Dynamics of Nonlinear Editor: G. Harbeke Systems 58 The Recursion Method and Editors: G. Benedek, H. Bilz, Its Applications and R. Zeyher Editors: D. Pettifor and D. Weaire 48 Magnetic Phase Transitions Editors: M. Ausloos and R. 1. Elliott 59 Dynamical Processes and 49 Organic Molecular Aggregates, Electronic Ordering on Solid Surfaces Editors: A. Yoshimori and M. Tsukada Excitation and Interaction Processes Editors: P. Reineker, H. Haken, 61 Localization, Interaction, and and H. C. Wolf Transport Phenomena 50 Multiple Diffraction of X-Rays in Crystals Editors: B. Kramer, G. Bergmann, By Shih-Lin Chang and Y. Bruynseraede Volume 1-39 are listed on the back inside cover Localization, Interaction, and Transport Phenomena Proceedings of the International Conference, August 23-28, 1984 Braunschweig, Fed. Rep. of Germany Editors: B. Kramer, G. Bergmann, and Y Bruynseraede With 125 Figures Springer- ¥e rlag Berlin Heidelberg New York Tokyo Professor Dr. Bernhard Kramer Physikalisch-Technische Bundesanstalt Braunschweig, Postfach 3345 D-3300 Braunschweig, Fed. Rep. of Germany Professor Dr. Gerd Bergmann Institut flir Festkorperforschung, Kernforschungsanlage lillich, Postfach 1913 D-5170 lillich, Fed. Rep. of Germany Professor Dr. Yvan Bruynseraede Laboratorium voor Vaste Stof-Fysika en Magnetisme, Celestijnenlaan 200 D B-3030 Leuven, Belgium Series Editors: Professor Dr. Manuel Cardona . Professor Dr. Peter Fulde Professor Dr. Hans-Joachim Queisser Max-Planck-Institut flir Festkorperforschung, Heisenbergstrasse 1 D-7000 Stuttgart 80, Fed. Rep. of Germany Organizing Committee B. Kramer (Chairman) (Physikalisch-Technische Bundesanstalt Braunschweig, RR.G.) G. Bergmann (Kernforschungsanlage Jti1ich, RR.G.) Y. Bruynseraede (Universiteit Leuven, Belgium) L. Van Gerven (Universiteit Leuven, Belgium) W. Gey (Technische Universitiit Braunschweig, RR.G.) Advisory Committee R. Huguenin, Switzerland L. P. Gor'kov, USSR W. Weller, G.D.R. M. Pepper, U.K. A. A. Abrikosov, USSR M. Ya. Az bel', Israel P. Chaudhari, USA A. G. Aronov, USSR G. Deutscher, Israel P. W. Anderson, USA A. A. Rogachev, USSR S. Kobayashi, Japan E. Abrahams, USA R. Taylor, Canada S. Hikami, Japan A. W. Overhauser, USA W. GOtze, RR.G. P. Wyder, The Netherlands Secretary Elisabeth Meyer (Physikalisch·Technische Bundesanstalt Braunschweig, RR.G.) Sponsors The conference was organized under the auspices of the Deutsche Physikalische Gesellschaft Financial support was obtained from: Volksbank Braunschweig Physikalisch-Technische Bundesanstalt Braunschweig Firma Richard Borek Braunschweig Stadt Braunschweig IBM Deutschland ISBN-13:978-3-642-82518-7 e-ISBN-13:978-3-642-82516-3 DOl: 10.1007/978-3-642-82516-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copy right Law, where copies are made for other than private use, a fee is payable to ''Verwertungsgesellschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1985 . Softcover reprint of the hardcover 1st edition 1985 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2153/3130-543210 Preface LITPIM When we first had the idea of organizing the International Conference on Localization, Interaction, and Transport Phenomena in Impure Metals we expected to bring together at most a hundred physicists. The fact that more than a hundred and fifty participated clearly shows that the topic of the meeting was of great interest to an important fraction of the solid state physics community. In fact, remembering that the localization problem is already a quarter of a century old, it is quite amazing to see how, during the last five years, new and very successful theoretical models emerged which were confirmed by sometimes ingenious experiments. The number of groups involved in the study of localization or related problems in the transport properties of matter even seems to be increasing. The main purpose of this conference was to review the present status of activities in the localization field and hopefully to stimulate new ideas. A study of the Conference Proceedings ascertains that we were successful in reaching these two goals. Moreover, the presence of the authors of the about ninety contributed papers published in the supplement volume assured the very lively atmosphere which characterizes successful conferences. We think that this was the most important ingredient for achieving the second goal in particular. We thank our sponsors for their support, which was given unreluctantly and generously. Especially, we gratefully acknowledge the hospitality of the PTB and the city of Braunschweig during the time of the meeting. With out this help ,the organization of the conference would hardly have been possible in the form which we all have experienced. We also thank the nu merous people who have contributed by helping during the preparation of the conference and in the daily affairs, especially Wolfgang Woger, Lud wig Schweitzer, and Robert Johnston. In particular, we would also like to thank Mr. Wolfgang Pogrzeba, who was responsible for the technical ar rangements, and our conference secretary, Mrs. Elisabeth Meyer. She was extremely efficient in organizing all the details of LITPIM, preparing the Conference Program, the Abstract Booklet, and the Proceedings. It would have been very hard, if not impossible, to run the meeting without her continuous and extremely reliable work. Braunschweig, B. Kramer November 1984 G. Bergmann Y. Bruynseraede v Contents Localization, Interaction, and Transport Phenomena in Impure Metals. An Introduction By B. Kramer, G. Bergmann, and Y. Bruynseraede (With 4 Figures) 1 Part I Invited Papers Some Unresolved Questions in the Theory of Localization By P. W. Anderson (With 3 Figures) . . . . . . . . . . . . . . . . . .. 12 Localization and Interaction in Quasi-Two-Dimensional Metallic Films By Shun-ichi Kobayashi (With 6 Figures) . . . . . . . . . . . . . 18 Weak Localization in Silicon Mosfets: Isotropic and Anisotropic Two-Dimensional Electron Gases By D.J. Bishop, D.C. Tsui, and R.C. Dynes (With 9 Figures) ... 31 Transport as a Consequence of Incident Carrier Flux By R. Landauer (With 3 Figures) .......... . . .. 38 Interaction Effects in Weakly Localized Regime of Metallic Films By H. Fukuyama (With 9 Figures) . . . . . . . . . . . . . . . .. . 51 The Conductor Insulator Transition in Strongly Disordered Systems By W. Gotze (With 8 Figures) . . . . . . . . . . . . . . . . . . . . . . 62 Recent Developments in the Metal-Insulator Transition By G.A. Thomas and M.A. Paalanen (With 10 Figures) ....... 77 The Scaling Theory of Localisation By A. MacKiI,mon (With 2 Figures) ...... 90 Anderson Transition and Nonlinear a-Model By F. Wegner ...... 99 Localization and Superconductivity By G. Deutscher, A. Palevski, and R. Rosenbaum (With 8 Figures) . 108 Aperiodic Strl!cture in the Magnetoresistance of Very Narrow Metallic Rings and Lines. By R.A. Webb, S. Washburn, C.P. Umbach, and R.B. Laibowitz (With 4 Figures) . . . . . . " . . . . . . . . . . . . 121 Theory of Weak Localization and Superconducting Fluctuations By S. Maekawa (With 4 Figures) ................. . 130 VII Preparation and Physics of Novel Microstructures for Localization Studies By M.R. Beasley, S. Bending, and J. Graybeal (With 8 Figures) ... 138 Fluctuation and Localization Effects in Quasi-One-Dimensional Metallic Structures By D.E. Prober, S. Wind, and P. Santhanam (With 5 Figures) ... 148 Theory of Fluctuation Phenomena in Kinetics By M. Ya Azbel' .............................. 162 Quasi One-Dimensional Transport in Narrow Silicon Accumulation Layers. By C.C. Dean and M. Pepper (With 6 Figures) ........ 169 Experiments on Localization and Interaction in a Strong Magnetic Field. By G. Ebert (With 11 Figures) .............. . . . . 178 Localization and the Integral Quantum Hall Effect By A.M.M. Pruisken (With 2 Figures) ................. 188 Quantum Hall Effect and Additional Oscillations of Conductivity in Weak Magnetic Fields By D.E. Khmel'nitskii (With 2 Figures) ................. 208 Electron-Phonon Scattering in Dirty Metals By A. Schmid (With 8 Figures) ..................... 212 Electron Scattering Times in Thin Metal Films: Experimental Results By C. Van Haesendonck, M. Gijs, and Y. Bruynseraede (With 8 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Inelastic Lifetime of Conduction Electrons as Determined from Non-Localization Methods By J.E. MO,?ij and T.M. Klapwijk (With 5 Figures) .......... 233 Comments of Some Aspects of the Localization and Interaction Problem. By E. Abrahams . . . . . . . . . . . . . . . . . . . . .... 245 Part II Titles of Contributed Papers Localization in One Dimension . . . . . .252 Weak Localization in Three Dimensions .253 Flux Quantization in Normal Rings .254 Two-Dimensional Systems ..... . .255 Localization, Magnetism and Superconductivity. .256 Metal-Insulator Transition. .257 VIII Localization and Interaction in the Magnetic Field .259 Inelastic Scattering Times .260 Conference Photograph .261 Index of Contributors . .263 IX Localization, Interaction, and Transport Phenomena in Impure Metals. An Introduction B. Kramer Physikalisch-Technische Bundesanstalt, Bundesallee 100 0-3300 Braunschweig, Fed. Rep. of Germany G. Bergmann Institut fUr Festkorperforschung der KFA JUlich, Postfach 1913 0-5170 JUlich, Fed. Rep. of Germany Y. Bruynseraede Laboratorium voor Vaste Stof-Fysika en Magnetisme, Universiteit Leuven Celestijnenlaan 2000, B-3030 Leuven, Belgium 1. Overview Transport properties of solids are determined by disorder due to the presen ce of impurities or imperfections of the lattice, by various interaction ef fects such as electron-electron, electron-phonon interaction and by spin-de pendent processes due to spin-orbit and spin-spin coupling. At room tempera ture the details of these interactions are unimportant. They are usually in corporated into one of several mean free paths. As the temperature is lowered these effects become however more and more important. Thus the study of the transport properties of solids is a typical field of low-temperature physics. A number of "classical" low-temperature effects in metals are a sig nature of the presence of well defined microscopic processes [1]. The residuaZ resistance is due to impurity scattering, the Kondo effect to spin scattering, and the "classical" temperature-dependence of the resistance, T5, is within Bloch's theory described as an electron-phonon effect. There are "classical" rules, how to combine various scattering processes, such as Matthiesen's rule. Many of these effects and "laws" can be derived neglec ting quantum mechanical interference effects within the frame work of the relaxation-time approximation. One of the main subjects of the research du ring the past thirty years has been to include quantum mechanics into a microscopic transport theory. This goal is not yet reached. However, one very important step has become more and more transparent during the past five years: The problem of localization due to disorder has been formulated in a way allowing systematic theoretical, and what is perhaps more impor tant, experimental studies. In addition,one may expect fruitful interaction with the modern technology of very large-scale integration (VLSI). It is now little more than 25 years ago that P.W. Anderson published "The Absence of Diffusion in Certain Random Lattices" [2]. He simul taneously formulated the problem, made the link between localization and transport, and gave the first quantitative estimate for the critical disor der for the transition between the diffusive and the non-diffusive regimes. Localization may be viewed as one of the most fundamental quantum mechani cal phenomena related to real condensed matter. The most simple model to discuss is that of a spinless, noninteracting particle moving in a random potential. As it forms the basis for the far more complicated theory inclu ding spin and interactions/we want to discuss its qualitativ~ aspects in some detail in the following sections. More details will be presented by the various authors in this volume. 2. Definition of Localization In this section we consider a system at zero temperature. For a classical particle in a random potential it is comparatively simple to decide whether its motion is restricted to finite portions of the space (Fig. 1). v(x) £2 ----------------------- .%1 X2 ~r-~--~r.~-+;-----~--~~X Fig. 1: Random potential If the energy of a particle is higher than Eo it can move through the whole space. On the other hand, if the energy is smaller than Eo, say EI , the motion is restricted to finite intervals, (Xl' X2)' (X3' X4), etc. In this case, one would assign to Eo a mobility edge. For the corresponding quantum mechanical problem the situation is more complicated for two rea sons: Firstly, there is the tunnel effect, which allows the particle to tunnel through the potential wells, thus delocalizing the particle. Second ly, there might be interference effects within the wave function scattered by the random potential. These may lead to localization of the particle via destructive superposition for energies above Eo. Thus, quantum mechanically, the conditions for localization are not as simple as in classical mechanics. An example for the first effect, delocalization due to tunneling, are the Bloch states in perfect crystals, which can be found in every text book of solid state physics. An example for localization via interference is the quantum mechanical behaviour of a particle in a one-dimensional random po tential. In this case only localized states occur, independent of the mag nitude of the disorder and/or the energy of the particle [3]. We have deliberately used the words "localization", "delocalization", and "disorder" without further details. Let us now specify what we mean bv localization. One of the interestinQ asoects of the oroblem of localization is the fact that it depends strongly on the dimensionality of the system. In a hypercube of volume Ld all states are d-dimensional pla ne waves, either standing or propagating, depending upon the boundary condi tions. These states are extended since the probability to find an electron at site x in a volume ddx is constant and equal to ddx/Ld.A trivial case of exponential localization is obtained if a charged nucleus is placed somewhere within the hypercube. A bound electron will be restricted to a volume around the nucleus. The corresponding probability density is exponentially decrea sing far away from the nucleus. If we introduce however a random potential v(x) into the hypercube the situation is more complicated. First of all we have to specify the potential. This is usually done by replacing the system by a statistical ensemble, which is characterized by a probability distribution. In the case of a Gaussian white noise potential, v(x), one has 2
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