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 v similar to 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.