Critical Level Statistics in Two-Dimensional Disordered Electron Systems

Abstract

The level statistics in two dimensional disordered electron systems inmagnetic fields(unitary ensemble) or in the presence of strong spin-orbit scattering(symplectic ensemble) are investigated at the Anderson transitionpoints. The level spacing distribution functions P(s) are found to beindependent of the system size or of the type of the potentialdistribution, suggesting universality. They behave as s² in thesmall s region in the former case, while increase proportional tos⁴ is seen in the latter.