Metal-insulator transition in three-dimensional semiconductors

TL;DR

This paper models the metal-insulator transition in 3D semiconductors using a random gap approach, identifying a continuous phase transition characterized by spontaneous symmetry breaking and critical exponents that match experimental crossover behaviors.

Contribution

It introduces a random gap model to describe the transition, highlighting the role of spontaneous symmetry breaking and providing critical exponents consistent with experiments.

Findings

Transition is continuous with exponent 1 at criticality

Spontaneous symmetry breaking distinguishes metallic from insulating phases

Exponent varies around 0.6 away from critical point

Abstract

We use a random gap model to describe a metal-insulator transition in three-dimensional semiconductors due to doping and find a conventional phase transition, where the effective scattering rate is the order parameter. Spontaneous symmetry breaking results in metallic behavior, whereas the insulating regime is characterized by the absence of spontaneous symmetry breaking. The transition is continuous for the average conductivity with critical exponent equal to 1. Away from the critical point the exponent is roughly 0.6, which may explain experimental observations of a crossover of the exponent from 1 to 0.5 by going away from the critical point.