Coulomb drag between parallel two-dimensional electron systems

Abstract

The Coulomb contribution to the temperature-dependent rate of momentum transfer, 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{D}}$, between two electron systems in parallel layers is determined by setting up two coupled Boltzmann equations, with the boundary condition that no current flows in the layer where an induced voltage is measured. The effective Coulomb interaction between the layers is determined self-consistently, allowing for the finite thickness of the layers. As T\ensuremath{\rightarrow}0, we find that 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{D}}$${\mathit{T}}^{2}$ approaches a constant value. At higher temperatures, 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{D}}$${\mathit{T}}^{2}$ exhibits a maximum at T=${\mathit{T}}_{\mathrm{max}}$ and then decreases as 1/T with increasing temperature. The value of ${\mathit{T}}_{\mathrm{max}}$ depends on the layer separation d according to ${\mathit{T}}_{\mathrm{max}}$\ensuremath{\propto}${\mathit{d}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$, where \ensuremath{\alpha}\ensuremath{\simeq}0.8. The overall magnitude of the calculated 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{D}}$ is approximately one-half of the results of a recent experiment, suggesting that other mechanisms of momentum transfer may be important.