Anderson localization of two-dimensional Dirac fermions: a perturbative approach

TL;DR

This paper investigates Anderson localization in 2D Dirac fermions under strong disorder, revealing localization along a semi-infinite line with a localization length inversely related to scattering rate, using a novel perturbative graphical approach.

Contribution

It introduces a perturbative graphical method to analyze Anderson localization in 2D Dirac fermions with strong randomness, highlighting the localization behavior and length dependence.

Findings

Localization occurs along a semi-infinite line

Localization length is inversely proportional to scattering rate

Graphical representation involves entangled random walks and three-vertices

Abstract

Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random walks and three-vertices which connect three different types of propagators. This approach indicates Anderson localization along a semi-infinite line, where the localization length is inversely proportional to the scattering rate.