Edge states in a thin film of disordered topological insulator

A thin-film geometry of nonmagnetic or magnetic topological insulator (TI) alters its topological properties depending on the thickness of the film and the strength of the magnetic coupling, and can exhibit the quantum spin Hall (QSH) effect as well as the quantum anomalous Hall (QAH) effect. In this study, we pursue a quantitative investigation of effects of nonmagnetic disorder on thin-film TIs in all the possible topological phases. The results show that strong enough disorder induces a topological phase transition and generically creates metallic helical edge states featuring the QSH phase before all electronic states are eventually localized. In the thermodynamic limit, the localization–delocalization transition in the disorder-induced QSH phase is in the unitary universality class with nontrivial Chern numbers. In a finite-size system, topologically protected edge states persist unless the mobility gap collapses. It is also demonstrated that edge states extend over a macroscopic distance in the middle of the mobility gap whereas they are strongly localized near the mobility edge because of mixing with bulk states. (author)