Mutual drag of two- and three-dimensional electron gases in heterostuctures.

Abstract

Mutual drag of two-dimensional (2D) and 3D electron gases in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterostructures is considered. The main purpose of the paper is to explain the recent experiment of Solomon et al. [Phys. Rev. Lett. 63, 2508 (1989)] in which a current in the channel induced a current in the gate and the latter changed its sign when temperature decreased. It is shown that Coulomb mutual scattering gives rise to two mechanisms of the current induction. The first of them is the direct momentum transfer between the 2D and 3D electron gases and induces a current in the gate in the same direction as that in the channel. The second mechanism is connected with the presence of a temperature gradient in the channel due to the Peltier effect on the contacts. Energy exchange between the electron gases transfers the temperature gradient to the gate where it induces a thermocurrent in the direction opposite to the current in the channel. At high temperatures the temperature gradient in the gate is small because of efficient energy exchange between the 3D electron gas and the lattice so that the current due to the direct momentum transfer dominates. When temperature decreases, the number of phonons participating in scattering processes with 3D electrons drops off (the Bloch-Gr\"uneisen regime sets in), and the energy transferred from the 3D electron gas to the lattice decreases. As a result the thermocurrent dominates and the total current changes its sign. The theory explains the principal features of the experiment.