Weak localization properties of the dopedZ2topological insulator

Abstract

Localization properties of the doped ${Z}_{2}$ topological insulator are studied by weak localization theory. The disordered Kane-Mele model for graphene is taken as a prototype and analyzed with attention to effects of the topological mass term, intervalley scattering, and the Rashba spin-orbit interaction. The known tendency of graphene to antilocalize in the absence of intervalley scattering between $K$ and ${K}^{\ensuremath{'}}$ points is naturally placed as the massless limit of the Kane-Mele model. The latter is shown to have a unitary behavior even in the absence of magnetic field due to the topological mass term. When intervalley scattering is introduced, the topological mass term leaves the system in the unitary class, whereas the ordinary mass term, which appears if A and B sublattices are inequivalent, turns the system to weak localization. The Rashba spin-orbit interaction in the presence of $K\text{\ensuremath{-}}{K}^{\ensuremath{'}}$ scattering drives the system to weak antilocalization in sharp contrast to the ideal graphene case.