Drude weight and optical conductivity of a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions

TL;DR

This paper provides a detailed theoretical analysis of the Drude weight and optical conductivity in a two-dimensional heavy-hole gas with $k$-cubic spin-orbit interactions, revealing unique behaviors distinct from electron gases.

Contribution

It introduces a comprehensive theoretical framework for understanding how $k$-cubic spin-orbit couplings affect optical properties and Drude weight in 2D heavy-hole gases, highlighting differences from electron gases.

Findings

Drude weight deviates from linear density dependence at high densities and strong couplings.

Optical conductivity remains non-zero even with equal Rashba and Dresselhaus couplings due to Berry phase effects.

Optical transition threshold is an order of magnitude smaller than in electron gases.

Abstract

We present detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas(2DHG) with $k$-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of $k$-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with $k$-linear spin-orbit couplings. For large hole density and strong $k$-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with $k$-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of $k$-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.