Optical selection rules in topological insulators Bi$_2$Sb$_3$, Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$

TL;DR

This paper investigates the optical selection rules in topological insulators Bi2Sb3, Bi2Se3, Bi2Te3, and Sb2Te3 using group theory, revealing polarization dependencies and calculating photoelectron spin polarizations.

Contribution

It introduces a new technique for analyzing surface-to-bulk state transitions and provides a general rule for representation products in the Brillouin zone.

Findings

Optical transitions depend on light polarization at specific Brillouin zone points.

Surface and bulk state transitions follow specific symmetry-based selection rules.

Electron spin polarization of photoelectrons is calculated at the b0 point.

Abstract

We performed group theoretical investigation of symmetries of excitations in topological insulators \ce{Bi2Sb3}, \ce{Bi2Te3}, \ce{Bi2Se3} and \ce{Sb2Te3}, focusing on selection rules for optical processes. Electronic transitions of bulk states to bulk states, surface states to surface states and bulk states to surface states are studied over the entire Brillouin zone. A new technique is used to deal with transitions between surface states and bulk states. Time reversal symmtry is also included in the analysis. Our results show that only (\Gamma), (\Lambda) and (M) points of the Brillouin zone would depend on light polarization for transitions between bulk states and surface states. As an example of application, electron spin polarizations of photoelectrons are calculated at (\Gamma) point. A general rule for the direct product between the representation at an arbitrary point in the Brillouin zone with itself is presented.