Criticality of the metal–topological insulator transition driven by disorder

Employing scaling analysis of the localization length, we deduce the critical exponent of the metal–topological insulator transitions induced by disorder. The obtained exponent $\nu \sim 2.7$ 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.