The intrinsic inter-band optical conductivity of a C$_{2v}$ symmetric topological insulator

TL;DR

This paper analytically derives the optical conductivity of a C$_{2v}$ symmetric topological insulator, revealing conditions for vanishing inter-band conductivity and extending results to the anisotropic Dirac cones of SmB$_{6}$.

Contribution

It provides an analytical expression for the optical conductivity of C$_{2v}$ topological insulators and explores the effects of Dresselhaus and Rashba parameters, including for topological Kondo insulator SmB$_{6}$.

Findings

Inter-band conductivity vanishes when Dresselhaus equals Rashba strength.

Derived frequency-dependent optical conductivity for SmB$_{6}$.

Identified conditions for persistent spin helix state.

Abstract

In this work we analytically investigate the longitudinal optical conductivity of the C$_{2v}$ symmetric topological insulator. The conductivity expressions at $ T = 0 $ are derived using the Kubo formula and expressed as a function of the ratio of the Dresselhaus and Rashba parameters that characterize the low-energy Hamiltonian. We find that the longitudinal inter-band conductivity vanishes when Dresselhaus and Rashba parameters are equal in strength, also called the persistent spin helix state. The calculations are extended to obtain the frequency-dependent real and imaginary components of the optical conductivity for the topological Kondo insulator SmB$_{6}$ which exhibits C$_{2v}$ symmetric and anisotropic Dirac cones hosting topological states at the $ \bar{X} $ point on the surface Brillouin zone.