Localization, Interaction, and Transport Phenomena in Impure Metals. An Introduction

Overview

Transport properties of solids are determined by disorder due to the presence of impurities or imperfections of the lattice, by various interaction effects such as electron-electron, electron-phonon interaction and by spin-dependent processes due to spin-orbit and spin-spin coupling. At room temperature the details of these interactions are unimportant. They are usually incorporated 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 signature of the presence of well defined microscopic processes [1]. The residual 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 neglecting quantum mechanical interference effects within the frame work of the relaxation-time approximation. One of the main subjects of the research during 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 important, 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 simultaneously formulated the problem, made the link between localization and transport, and gave the first quantitative estimate for the critical disorder for the transition between the diffusive and the non-diffusive regimes. Localization may be viewed as one of the most fundamental quantum mechanical 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 including spin and interactions, we want to discuss its qualitative aspects in some detail in the following sections. More details will be presented by the various authors in this volume.