Localization And Metal Insulator Transitions

This volume and its two companion volumes, entitled Tetrahedrally-Bonded Amorphous Semiconductors and Physics of Disordered Materials, are our way of paying special tribute to Sir Nevill Mott and to express our heartfelt wishes to him on the occasion of his eightieth birthday. Sir Nevill has set the highest standards as a physicist, teacher, and scientific leader. Our feelings for him include not only the respect and admiration due a great scientist, but also a deep affection for a great human being, who possesses a rare combination of outstanding personal qualities. We thank him for enriching our lives, and we shall forever carry cherished memories of this noble man. Scientists best express their thanks by contributing their thoughts and observations to a Festschrift. This one honoring Sir Nevill fills three volumes, with literally hundreds of authors meeting a strict deadline. The fact that contributions poured in from all parts of the world attests to the international cohesion of our scientific community. It is a tribute to Sir Nevill's stand for peace and understanding, transcending national borders. The editors wish to express their gratitude to Ghazaleh Koefod for her diligence and expertise in deciphering and typing many of the papers, as well as helping in numerous other ways. The blame for the errors that remain belongs to the editors.

This is a second edition of a classic book. Written by the late, great Sir Nevill Mott (Britain's last Nobel Prize winner for Physics), Metal Insulator Transitions has been greatly updated and expanded to further enhance its already enviable reputation.

This volume and its two companion volumes, entitled Tetrahedrally-Bonded Amorphous Semiconductors and Physics of Disordered Materials, are our way of paying special tribute to Sir Nevill Mott and to express our heartfelt wishes to him on the occasion of his eightieth birthday. Sir Nevill has set the highest standards as a physicist, teacher, and scientific leader. Our feelings for him include not only the respect and admiration due a great scientist, but also a deep affection for a great human being, who possesses a rare combination of outstanding personal qualities. We thank him for enriching our lives, and we shall forever carry cherished memories of this noble man. Scientists best express their thanks by contributing their thoughts and observations to a Festschrift. This one honoring Sir Nevill fills three volumes, with literally hundreds of authors meeting a strict deadline. The fact that contributions poured in from all parts of the world attests to the international cohesion of our scientific community. It is a tribute to Sir Nevill's stand for peace and understanding, transcending national borders. The editors wish to express their gratitude to Ghazaleh Koefod for her diligence and expertise in deciphering and typing many of the papers, as well as helping in numerous other ways. The blame for the errors that remain belongs to the editors.

The discovery of the quantized and fractional Quantum Hall Effect phenomena is among the most important physics findings in the latter half of this century. The precise quantization of the electrical resistance involved in the quantized Hall effect phenomena has led to the new definition of the resistance standard and has metrologically affected all of science and technology. This resource consists of contributions from the top researchers in the field who present recent experimental and theoretical developments. Each chapter is self-contained and includes its own set of references guiding readers to original papers and further reading on the topic.

This book presents a review of theoretical and experimental work on the problem of the interplay of Anderson localization and superconductivity in strongly disordered systems. Superconductivity persists close to disorder-induced metal-insulator transition in a number of real systems, e.g. amorphous metals and compounds, systems disordered by fast neutron irradiation, systems with impurities, etc. High temperature superconductors are especially interesting from this point of view, as the experiments with controllable disordering may provide important clues to the nature of electronic states in these systems.The book starts with a brief discussion on modern aspects of localization theory, including the basic concept of scaling, self-consistent theory of localization and interaction effects. After that it analyzes disorder effects on Cooper pairing and superconductivity transition temperature as well as Ginzburg-Landau equations for superconductors that are close to the Anderson transition. A necessary generalization of the usual theory of dirty superconductors is formulated which allows one to analyze anomalies of the main superconducting properties close to disorder-induced metal-insulator transition. Finally, the book reviews a number of experiments demonstrating superconductivity close to the Anderson transition, in both traditional and high c superconductors."

Little do we reliably know about the Mott transition, and we are far from a complete understanding of the metal --insulator transition due to electr- electron interactions. Mott summarized his basic ideas on the subject in his wonderful book Metal--Insulator nansitions that first appeared in 1974 11. 1). In his view, a Motk insulator displays a gap for charge-carrying excitations due to electron cowelations, whose importance is expressed by the presence of local magnetic moments regardless of whether or not they are ordered. Since the subject is far from being settled, different opinions on specific aspects of the Mott transition still persist. This book naturally embodies my own understanding of the phenomenon, inspired by the work of the late Sir Kevill Mott. The purpose of this book is twofold: first, to give a detailed presen- tion of the basic theoretical concopts for Mott insulators and, second, to test these ideas against the results from model calculations. For this purpose the Hubbard model and some of its derivatives are best suited. The Hubbard model describes a Mott transition with a mere minimum of tunable par- eters, and various exact statements and even exact solutions exist in certain limiting cases. Exact solutions not only allow us to test our basic ideas, but also help to assess the quality of approxin~ate theories for correlated electron systems.

Localisation and Interaction covers the scaling theory of localization metal-insulator transitions, two-dimensional systems, interaction effects in impure metals, weak localization, critical point measurement, quantum wells, integer quantum Hall effects, magnetic field induced transitions, static and dynamic magnetic probes, band gap narrowing, and an experiment with the quantum Hall effects.