Scaling behavior of disordered lattice fermions in two dimensions

TL;DR

This paper investigates how disorder affects the localization length of two-dimensional lattice Dirac fermions, revealing different scaling regimes and phase transitions driven by randomness strength.

Contribution

It introduces a lattice model for Dirac fermions with tunable node degeneracy and analyzes the scaling behavior under random gaps using transfer-matrix methods.

Findings

Different scaling regimes identified for weak, intermediate, and strong disorder.

Transitions between regimes are characterized by one-parameter scaling.

Localization length behavior varies with disorder strength.

Abstract

We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within a numerical transfer-matrix approach. Depending on the strength of the randomness, there are different scaling regimes for weak, intermediate and strong disorder. These regimes are separated by transitions that are characterized by one-parameter scaling.