Direct Coulomb and phonon-mediated coupling between spatially separated electron gases

Momentum transfer due to electron-electron interaction between two quasi-two-dimensional electron gases, whose edges are separated by a distance d, is studied at low temperatures (T). The coupling between the gases results from the direct Coulomb (screened) interaction and from the interaction mediated by virtual phonon exchange. The former has a ${\mathit{T}}^2$ dependence and varies approximately as ${\mathit{d}}^{\mathrm{-}4}$ for large d. The latter depends very weakly on d and, combined with the former, accounts extremely well for the T and d dependences of the relaxation time as measured by Gramila et al. [Phys. Rev. Lett. 66, 1216 (1991)].