Spin-orbit interactions in two-dimensional electron liquids are responsible for many interesting transport phenomena in which particle currents are converted to spin polarizations and spin currents and viceversa. Prime examples are the spin Hall effect, the Edelstein effect, and their inverses. By similar mechanisms it is also possible to partially convert an optically induced electron-hole density wave to a spin density wave and viceversa. In this paper we present a unified theoretical treatment of these effects based on quantum kinetic equations that include not only the intrinsic spin-orbit coupling from the band structure of the host material, but also the spin-orbit coupling due to an external electric field and a random impurity potential. The drift-diffusion equations we derive in the diffusive regime are applicable to a broad variety of experimental situations, both homogeneous and non-homogeneous, and include on equal footing skew scattering and side-jump from electron-impurity collisions. As a demonstration of the strength and usefulness of the theory we apply it to the study of several effects of current experimental interest: the inverse Edelstein effect, the spin-current swapping effect, and the partial conversion of an electron-hole density wave to a spin density wave in a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings, subject to an electric field.
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