Typical-Medium Theory of Mott-Anderson Localization

TL;DR

This paper introduces the Typical-Medium Theory, a unified framework that captures both Mott and Anderson localization mechanisms in the metal-insulator transition by focusing on the dynamical order parameter related to electron escape rates.

Contribution

It develops the Typical-Medium Theory to describe the combined effects of Mott and Anderson localization, addressing the lack of a static order parameter and providing new insights into the transition's two-fluid nature.

Findings

The theory identifies the typical escape rate as the key dynamical order parameter.

It offers a unified description of Mott and Anderson localization mechanisms.

The approach reveals a two-fluid character in the Mott-Anderson transition.

Abstract

The Mott and the Anderson routes to localization have long been recognized as the two basic processes that can drive the metal-insulator transition (MIT). Theories separately describing each of these mechanisms were discussed long ago, but an accepted approach that can include both has remained elusive. The lack of any obvious static symmetry distinguishing the metal from the insulator poses another fundamental problem, since an appropriate static order parameter cannot be easily found. More recent work, however, has revisited the original arguments of Anderson and Mott, which stressed that the key diference between the metal end the insulator lies in the dynamics of the electron. This physical picture has suggested that the "typical" (geometrically averaged) escape rate from a given lattice site should be regarded as the proper dynamical order parameter for the MIT, one that can naturally describe both the Anderson and the Mott mechanism for localization. This article provides an overview of the recent results obtained from the corresponding Typical-Medium Theory, which provided new insight into the the two-fluid character of the Mott-Anderson transition.