Disordered two-dimensional electron systems with chiral symmetry

TL;DR

This paper reviews numerical studies on disordered 2D electron systems with chiral symmetry, focusing on density of states, Lyapunov exponents, and critical behavior near the quantum critical point at E=0.

Contribution

It provides a comprehensive review of numerical results on chiral symmetric disordered systems, highlighting critical phenomena and potential non-universality of exponents.

Findings

Peaks and depressions in the density of states near E=0

Distribution patterns of critical conductances

Indications of non-universality in critical exponents for some models

Abstract

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.