Anderson transitions in disordered two-dimensional lattices

TL;DR

This paper investigates the Anderson transition in various two-dimensional lattices by analyzing energy level statistics and electrical conductivity, revealing a universal complexity parameter governing localization phenomena.

Contribution

It introduces a unified framework using a single complexity parameter to describe localization transitions across different 2D lattice types.

Findings

Identifies a clear delocalization to localization transition with increasing disorder.

Shows the existence of a universal complexity parameter linking different lattice systems.

Demonstrates that statistical measures align when scaled by this parameter.

Abstract

We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagom\'e, the square, and the triangular lattice. By calculating the well-known statistical measures viz., nearest neighbor spacing distribution, number variance, the partition number and the dc electrical conductivity from Kubo-Greenwood formula, we show that there is clearly a delocalization to localization transition with increasing disorder. Though the statistics in different lattice systems differs when compared with respect to the change in the disorder strength only, we find there exists a single complexity parameter, a function of the disorder strength, coordination number, localization length, and the local mean level spacing, in terms of which the statistics of the fluctuations matches for all lattice systems at least when the Fermi energy is selected from the bulk of the energy levels.