A Band of Critical States in Anderson Localization at Strong Magnetic Field with Random Spin-Orbit Scattering

TL;DR

This study investigates the nature of localization-delocalization transitions in a 2D electron system under strong magnetic fields with disordered potentials and spin-orbit coupling, revealing a novel critical state band with Berezinskii-Kosterlitz-Thouless-like behavior.

Contribution

It uncovers a new band of critical states in Anderson localization with fully random spin-orbit coupling, differing from the standard Landau band structure, and characterizes its unique transition behavior.

Findings

Presence of a critical state band with fractal structure

Divergence of localization length as a stretched exponential near critical energy

Distinct behavior for uniform versus fully random spin-orbit coupling

Abstract

Anderson localization problem for non-interacting two-dimensional electron gas subject to strong magnetic field, disordered potential and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on the nature of the spin-orbit coupling (uniform or fully random). For uniform spin-orbit coupling (such as Rashba coupling), there is a band of extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy $E_c$, the localization length diverges as $\xi(E) \propto\exp(\alpha/\sqrt{|E-E_c|})$, a behavior which, along with the band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.