# Ebook: Physics of Metal-Nonmetal Transitions

**Description**

Material undergoes the transformation from metal to non-metal or from non-metal to metal when environmental conditions, such as temperature and pressure, or the percentages of constituent components are changed. Such a transition is known as the metal-nonmetal (M-NM) transition.

This book, 'The Physics of Metal – Nonmetal Transitions', explores the mechanisms so far discovered which cause the M-NM transition and presents a systematic discussion of them. All the mechanisms are discussed in terms of energy bands, and the band theory is introduced and explained in chapter 2. Once chapters 1 and 2 have been assimilated, the remaining chapters can be read independently of each other if required. The mechanisms discussed therein include the Peierls transition, the Bloch-Wilson transitions – types I and II respectively – the second of which was discovered by the author and her students. Subsequent chapters cover the Anderson transition and the Mott transition, and each chapter includes not only traditional theories, but also updated information about more recent research.

The book can be used either as a textbook for undergraduate and postgraduate students of science and technology or as an introductory treatise for researchers in a wide variety of fields.

**Preface**

A material will undergo the transformation from metal to non-metal or from non-metal to metal when environmental conditions, such as temperature and pressure, or the percentages of the constituent components change. Such a transition is generally called the metal-nonmetal (M-NM) transition. Several mechanisms have been described as the cause of the M-NM transition, and these mechanisms are classified into categories. Some previously published books have only dealt with these mechanisms more or less independently. With this situation in mind, the author decided to assemble all these mechanisms together in one book and to present a systematic discussion of them. The mechanisms for the M-NM transition that have been gathered include the Peierls transition in Chapter 3, the Bloch-Wilson transition – Types I and II respectively in Chapters 4 and 5, the Anderson transition in Chapter 6, and the Mott transition in Chapter 7.

The characteristic aspect of this book is the way in which these mechanisms are dealt with as regards the M-NM transition: in terms of the energy bands. The aforementioned transition mechanisms are discussed on the same grounds, and an introductory explanation of the band theory is given in Chapter 2.

A reader, after acquiring the fundamental knowledge in Chapters 1 and 2, can study each chapter from Chapter 3 to 7 independently of one another. The discussions in Chapter 3 concerning the Peierls transition are, in particular, quite unrelated to the other chapters. Therefore, a reader can either regard Chapter 3 as the main purpose of reading this book or skip Chapter 3 and go onto any chapter from Chapter 4 to 7.

Chapter 3 includes some mathematical aspects, but they are not hard to understand. The author has made every effort to present the mathematical developments in such a way that the reader can grasp the idea without any trouble if he or she follows the equations in Chapter 3 step-by-step. All the derivations of the equations in connection with the theory of the Peierls transition are comprehensively given in Chapter 3 and in Appendixes C and D, and accordingly it is possible to learn the whole picture of the Peierls transition solely from this book.

Chapters 4 and 5 are considered to cover the stages for which, in particular, the analysis by means of energy bands demonstrates its real value. Chapters 6 and seven are devoted to the work of P W Anderson and N F Mott respectively in connection with the localisation theory in disordered systems (Chapter 6) and with the M-NM transition due to the electron correlation (Chapter 7). Appendix B deals with the percolation theory, which is a useful idea as the macroscopic mechanism for the M-NM transition.

All chapters include not only the traditional theories and methods but also updated information about more recent research to give the reader an idea of current trends.

Before concluding the preface, the author would like to point out that a number of new themes and new ways of analysing these themes are presented in this book, and that some of the subjects described here are completely original in themselves. Among other things, one subject presented in Chapter 5 is completely new. This subject concerns a completely novel mechanism for the M-NM transition, that is to say, the Type II Bloch-Wilson transition. This novel mechanism was, in fact, discovered by the author and her students.

The reader will feel at home following the discussions in this book if he or she has some knowledge of elementary quantum mechanics. The book could serve equally well as a textbook for undergraduate and postgraduate students in science and technology, or as an introductory treatise for researchers in a wide variety of fields.