Topological insulator ribbon: Surface states and dynamical response

TL;DR

This paper theoretically investigates the charge and spin distributions, optical response, and dynamical spin susceptibility of a topological insulator ribbon with a rectangular cross section, revealing unique properties due to surface state discretization.

Contribution

It introduces a detailed analysis of surface state discretization and dynamical responses in topological insulator ribbons, highlighting differences from ideal surface states.

Findings

Surface states discretize into subbands due to lateral confinement.

Charge and spin distributions differ from ideal surface states.

Dynamical spin susceptibility can identify appropriate models for Bi$_2$Se$_3$.

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 of the bulk band gap. The charge and spin distribution show interesting characters which are different from an ideal topological surface state. The effect of merging of four different surface states into the 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 the more adequate model for Bi$_2$Se$_3$.