Coupled electron-hole transport: Generalized random-phase approximation and density functional theory

Abstract

Coulomb coupling between spatially separated two-dimensional electron and hole gases, when an electric field is applied to only one of them, is studied as function of temperature and electron (hole) gas density. The coupling is described in the random-phase approximation (RPA) and in a generalized RFA (GRPA) which takes into account exchange processes to all orders of the Hartree-Fock potential within the Hubbard approximation [Phys. Rev. 111 (1958) 442; Proc. R. Soc. London A 243 (1957) 336]. Due to the exclusion principle at low densities, electrons (holes) of the same spin are kept so far apart that only electrons (holes) of different spin screen each other. The GRPA coupling is stronger than the RPA one and leads to a larger transimpedancc R T. The temperature dependence of R T agrees very well with that measured by Sivan et al. [1] for relatively high densities. The GRPA result for square wells is still below the experimental value, but it can be improved with a self-consistent calculation of the envelope function and of the mean separation between the gases.