Metal Insulator Transitions

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.

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.

When many particles come together how do they organize themselves? And what destroys this organization? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them. It captures the excitement and the controversies on topics at the forefront of research.

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.

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 text surveys the various aspects of the fundamental problem related to the metallic and non-metallic states of matter, a question physicists have been studying for almost 100 years. The book poses questions and challenges in this area, as well as highlighting present understandings of the topic. Topics covered by the book include physics of dense ionized metal plasmas; metallic hydrogen; pressure-induced metallization; the M-I transition in doped semiconductors; transport studies in doped semiconductors near the metal-insulator transition; new results in old oxides; metal-insulator transition in 3d transition metal perovskite oxides investigated by high-energy spectroscopies; alkali metal-alkali halide melts; hopping conductivity in granular metals revisited; superconductor-insulator transition in cuprates; molecular metals and superconductors; shear induced chemical reactivity; shear, co-ordination and metallization; quantum diffusion and decoherence; the Mott transition; recent results, more and surprises; Mott-Hubbard-Anderson models.

The present book on electrical, optical, magnetic and thermal properties of materials is in many aspects different from other introductory texts in solid state physics. First of all, this book is written for engineers, particularly materials and electrical engineers who want to gain a fundamental under standing of semiconductor devices, magnetic materials, lasers, alloys, etc. Second, it stresses concepts rather than mathematical formalism, which should make the presentation relatively easy to understand. Thus, this book provides a thorough preparation for advanced texts, monographs, or special ized journal articles. Third, this book is not an encyclopedia. The selection oftopics is restricted to material which is considered to be essential and which can be covered in a 15-week semester course. For those professors who want to teach a two-semester course, supplemental topics can be found which deepen the understanding. (These sections are marked by an asterisk [*]. ) Fourth, the present text leaves the teaching of crystallography, X-ray diffrac tion, diffusion, lattice defects, etc. , to those courses which specialize in these subjects. As a rule, engineering students learn this material at the beginning of their upper division curriculum. The reader is, however, reminded of some of these topics whenever the need arises. Fifth, this book is distinctly divided into five self-contained parts which may be read independently.

This book describes all aspects of the physics of transition metal compounds, providing a comprehensive overview of this diverse class of solids. Set within a modern conceptual framework, this is an invaluable, up-to-date resource for graduate students, researchers and industrial practitioners in solid-state physics and chemistry, materials science, and inorganic chemistry.