Anderson transition of two-dimensional spinful electrons in the Gaussian unitary ensemble

Abstract

We study the Anderson localization of disordered two-dimensional electron gases (2DEGs) on a square lattice subject to a perpendicular magnetic field $B$, random scalar potentials, and Rashba spin-orbit interactions. Our focus is on the weak magnetic field region, motivated by the intriguing question of how those extended states, existing in the absence of the magnetic field $(B=0)$ when the 2DEGs are the Gaussian symplectic ensemble, change with $B$. Using highly accurate numerical procedures based on the transfer matrix technique and the level statistics, we found that a metallic phase exists at weak magnetic fields, in contrast to the predictions of the one-parameter scaling theory that all states are localized at weak fields except at zero field, and the metallic phase evolves continuously into those at strong magnetic fields. A schematic phase diagram drawn in the field-energy plane elucidates the occurrence and evolution of extended states.