Topological Surface States: Hybridization and Transport from Theoretical Approaches

We review various topics on surface physics related with topological insulators. We first explain properties of topological insulators and associated surface Dirac cones. The surface states of topological insulators are different from conventional surface states in that they are characterized by topological numbers calculated from bulk wavefunctions. We then show physics related with hybridization of multiple Dirac cones from topological insulator surfaces. Such hybridization is realized in thin films, interfaces, and superlattices of topological insulators. In thin films the hybridization opens a gap in the surface states, whereas in interfaces and superlattices, the presence or absence of the surface gap and resulting band structure depends on system parameters and chiralities of the surface Dirac cones. Lastly we review the physics of Weyl and Dirac semimetals, and their implications in novel surface states.