Optical spectrum of a two-dimensional hole gas in the presence of spin-orbit interaction

Abstract

We present a theoretical study on how the Rashba type of spin splitting affects the optical spectrum of a two-dimensional hole gas (2DHG) realized from a $p$-type $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterojunction. The optical conductivity is evaluated on the basis of the Kubo formula and a standard random-phase approximation for hole-hole interaction in different spin branches. It is found that similar to the case of a spin-split two-dimensional electron gas (2DEG), the optical spectrum of a spin-split 2DHG depends strongly on two opticlike plasmon modes caused by collective excitation between two different spin branches. The position and width of the absorption spectrum relate directly to important spintronic coefficients. Thus, the spin splitting induced by the Rashba effect can be identified optically and important spintronic properties of a 2DHG can be measured via optical experiments. The results are also compared to those obtained for a spin-split 2DEG.