Topological insulator ribbon: Surface states and dynamical response

Abstract

We study theoretically the distributions of charge and spin polarization of a topological insulator ribbon, with a realistic rectangular cross section. Due to constriction in two lateral directions, the surface states discretize into a series of subbands inside the bulk band gap. The charge and spin distributions show interesting characters which are different from an ideal topological surface state. The effects of merging four different surface states into a new one as an entity are analyzed. Optical conductivity and dynamical spin susceptibility of the ribbon are studied. Different from a single ideal surface, the optical response and dynamical spin susceptibility of a ribbon do not have a clear correspondence. The dynamical spin susceptibility could be used to identify a more adequate model for Bi${}_{2}$Se${}_{3}$.