Criticality of the metal–topological insulator transition driven by disorder

Abstract

Employing scaling analysis of the localization length, we deduce the critical exponent of the metal--topological insulator transitions induced by disorder. The obtained exponent $\ensuremath{\nu}\ensuremath{\sim}2.7$ shows no conspicuous deviation from the value established for metal--ordinary insulator transitions in systems of the symplectic class. We investigate the topological phase diagram upon carrier doping to reveal the nature of the so-called topological Anderson insulator (TAI) region. The critical exponent of the metal--TAI transition is also first estimated, shown to be undistinguishable from the above value within the numerical error. By symmetry considerations we determine the explicit form of Rashba spin-orbit coupling in systems of ${C}_{4v}$ point group symmetry.