Weak localization and weak anti-localization in topological insulators

Weak localization and weak anti-localization are quantum interference effects in quantum transport in a disor-dered electron system. Weak anti-localization enhances the conductivity and weak localization suppresses the conductivity with decreasing temperature at very low temperatures. A magnetic field can destroy the quantum interference effect, giving rise to a cusp-like positive and negative magnetoconductivity as the signatures of weak localization and weak anti-localization, respectively. These effects have been widely observed in topological in-sulators. In this article, we review recent progresses in both theory and experiment of weak (anti-)localization in topological insulators, where the quasiparticles are described as Dirac fermions. We predicted a crossover from weak anti-localization to weak localization if the massless Dirac fermions (such as the surface states of topo-logical insulator) acquire a Dirac mass, which was confirmed experimentally. The bulk states in a topological insulator thin film can exhibit the weak localization effect, quite different from other system with strong spin-orbit interaction. We compare the localization behaviors of Dirac fermions with conventional electron systems in the presence of disorders of different symmetries. Finally, we show that both the interaction and quantum interference are required to account for the experimentally observed temperature and magnetic field dependenc