Diffusion of electrons in two-dimensional disordered symplectic systems

TL;DR

This paper numerically investigates electron diffusion in two-dimensional disordered systems with spin-orbit interactions, revealing critical behavior and implications for transport properties in metallic regimes.

Contribution

It provides new insights into the asymptotic behaviors and fractal structures affecting electron diffusion at critical points in disordered systems.

Findings

Auto-correlation function shows power-law decay with a non-conventional exponent.

Transport properties in the metallic regime align with the diffusion equation.

Fractal structures influence the critical behavior of electron wave functions.

Abstract

Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined. At the critical point, the auto-correlation function exhibits the power-law decay with a non-conventional exponent $\alpha$ which is related to the fractal structure in the energy spectrum and in the wave functions. In the metallic regime, the present results imply that transport properties can be described by the diffusion equation for normal metals.