Transport Equations and Spin-Charge Propagating Mode in a Two Dimensional Hole Gas with Spin-Orbit Coupling

We find that the spin-charge motion in a strongly confined two-dimensional hole gas (2DHG) supports a propagating mode with cubic dispersion apart from the diffusive mode due to momentum scattering. Propagating modes seem to be a generic property of systems with spin-orbit coupling. Through a rigorous Keldysh approach, we obtain the transport equations for any system with spin-orbit coupling that can be represented using spin- 1/2 matrices. We specialize to the 2DHG and analyze the behavior of the hole spin relaxation time, diffusion coefficients, and spin-charge coupled motion. We also confirm the value of the spin Hall conductivity in the ballistic regime and discuss the viability of the propagating mode.