Introduction to Metal-Insulator Transitions

TL;DR

This paper provides a comprehensive overview of metal-insulator transitions, discussing mechanisms, theoretical approaches, and experimental systems to understand electron localization and quantum critical behavior.

Contribution

It offers a comparative analysis of Mott and Anderson mechanisms, explores coexistence phenomena, and reviews theoretical perspectives and experimental clues in the study of metal-insulator transitions.

Findings

Different mechanisms can induce electron localization.

Coexistence of mechanisms leads to complex behaviors.

Theoretical approaches vary between weak and strong coupling.

Abstract

In this overview we provide a general introduction to metal-insulator transitions, with focus on specific mechanisms that can localize the electrons in absence of magnetic or charge ordering, and produce well defined quantum critical behavior. We contrast the physical picture of Mott, who emphasized the role of electron-electron interactions, and that of Anderson, who stressed the possibility of impurity-induced bound state formation, as alternative routes to arrest the electronic motion. We also describe more complicated situations when both phenomena play coexist, leading to meta-stability, slow relaxation, and glassy behavior of electrons. A critical overview of the available theoretical approaches is then presented, contrasting the weak-coupling perspective, which emphasizes diffusion-mode corrections, and the strong-coupling viewpoint, which stresses inhomogeneous phases and local correlation effects. We give specific examples of experimental systems, providing clues on what should be the most profitable path forward in unraveling the mystery of metal-insulator transitions.