Non-interacting electrons and the metal-insulator transition in 2D with correlated impurities

TL;DR

This paper explores how correlated impurities in 2D non-interacting electron systems can lead to a mobility edge and metallic behavior, contrasting with the insulating nature predicted by uncorrelated disorder models.

Contribution

It demonstrates that impurity correlations can induce a mobility edge in 2D systems, revealing a new regime where the system exhibits metallic behavior due to correlated disorder.

Findings

Presence of a mobility edge with correlated impurities

Intermediate regime shows metallic behavior with fluctuations

Strong localization occurs at large length scales

Abstract

While standard scaling arguments show that a system of non-interacting electrons in two dimensions and in the presence of uncorrelated disorder is insulating, in this work we discuss the case where inter-impurity correlations are included. We find that for point-like impurities and an infinite inter-impurity correlation length a mobility edge exists in 2D even if the individual impurity potentials are random. In the uncorrelated system we recover the scaling results, while in the intermediate regime for length scales comparable to the correlation length, the system behaves like a metal but with increasing fluctuations, before strong localization eventually takes over for length scales much larger than the correlation length. In the intermediate regime, the relevant length scale is not given by the elastic scattering length but by the inter-impurity correlation length, with important consequences for high mobility systems.