Topological Phases of Thin Films of Topological Insulators with and without Magnetic Fields.

The surface states residing at opposite surfaces of a topological insulator (TI) can hybridize if the thickness of the TI becomes comparable to their decay lengths, leading to a spectral gap. We investigate the conditions under which the resulting system has topological character, and study the topological properties of a free standing TI thin film. To this end, we develop a tunneling formalism for such TI-thin film-based heterostructures, and adapt it to the free standing situation. We find that accounting for the dependence of the decay lengths on the in-plane momentum is critical for accurately identifying the non-trivial topology. As a function of thickness, the film exhibits a sequence of transitions between gapped topological and trivial phases separated by states with a linear semi-metallic dispersion. In its topological phase, the thin film has edge states that carry a spin current with a spin component normal to the edge. In addition we explore the effect of in plane magnetic fields on these edge states.