Interacting drift-diffusion theory for photoexcited electron-hole gratings in semiconductor quantum wells

Phase-resolved transient grating spectroscopy in semiconductor quantum wells has been shown to be a powerful technique for measuring such an elusive quantity as the electron-hole drag resistivity $\rho_{eh}$, which depends on the Coulomb interaction between the carriers. In this paper we develop the interacting drift-diffusion theory, from which $\rho_{eh}$ can be determined, given the measured mobility of an electron-hole grating. From this theory we predict a cross-over from a high-excitation-density regime, in which the mobility has the ``normal" positive value, to a low-density regime, in which Coulomb-drag dominates and the mobility becomes negative. At the crossover point, the mobility of the grating vanishes.