Critical Level Statistics in Two-dimensional Disordered Electron Systems

TL;DR

This paper investigates the universal properties of level statistics at the Anderson transition in two-dimensional disordered electron systems, revealing distinct small-spacing behaviors in different symmetry classes.

Contribution

It demonstrates the universality of level spacing distributions at the transition and characterizes their behavior in unitary and symplectic ensembles.

Findings

Level spacing distributions are system size independent.

Distributions behave as s^2 in unitary ensemble.

Distributions behave as s^4 in symplectic ensemble.

Abstract

The level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The level spacing distribution functions $P(s)$'s are found to be independent of the system size or of the type of the potential distribution, suggesting the universality. They behave as $s^2$ in the small $s$ region in the former case, while $s^4$ rise is seen in the latter.