Quantification of the heavy-hole--light-hole mixing in two-dimensional hole gases

Abstract

We theoretically investigate heavy-hole--light-hole mixing in two-dimensional hole gases (2DHG). We restrict our analysis to the zone center, appropriate for the low-density regime, which leads to a simple description, analytical results, and physical insights. We identify two different types of hole-Hamiltonian terms concerning mixing. The first type changes the direction of the pure spinors, without admixing light-hole components. It is efficient for Rabi driving the heavy-hole spin. The second type induces mixing and changes the eigenvalues of the $g$-tensor. We analyze several measures that characterize the mixing quantitatively in Ge, Si, and GaAs, namely the $g$-factor, the light-hole weight in the wave function, the off-diagonal matrix elements in the Hamiltonian, and the strength of the induced spin-orbit interaction. We identify the canonical coordinate frame associated with a generic spin-3/2 Hamiltonian with time-reversal symmetry (TRS). In this coordinate frame, the mixing is quantified by a single parameter, the mixing angle $\vartheta$. We interpret it as the canonical (coordinate-frame and Hamiltonian-basis independent) measure of the heavy-hole--light-hole mixing. All the investigated mixing measures are simple functions of $\vartheta$. As an illustration, we use our model to analyze heavy-hole spin qubit $g$-tensor, dephasing, relaxation, and Rabi frequencies, interpreting the arising effects as due to rotations of the canonical frame and changes of the mixing angle $\vartheta$.