Thermopower of a double quantum well based on GaAs

Abstract

The resistivity and thermopower of a double quantum well have been investigated in the temperature range $0.3\ensuremath{-}4.2\mathrm{K}$ as a function of voltage applied to a top gate. As in previous studies, the resistivity showed a strong resonance when the carrier densities in each well were approximately the same. In contrast, neither diffusion nor phonon-drag thermopower showed any sensitivity to the resonance. We have calculated the thermopower based on a model of two independent two-dimensional electron gases (2DEG's) connected in parallel. In the case of phonon-drag thermopower, ${S}^{g},$ it was necessary to take into account the mutual screening of the electron-phonon interaction by electrons in each layer and also the local-field correction to the static dielectric function. We find that ${S}^{g}$ exhibits a ${T}^{5}$ dependence at low temperatures instead of the standard ${T}^{4}$ expected for single GaAs quantum wells. We also find that, for the lowest densities examined, the local-field correction enhances the magnitude of the calculated ${S}^{g}$ by over a factor of 2, in good agreement with experiment. As a check on the model of two independent 2DEG's we have also calculated ${S}^{g}$ at resonance taking into account interwell coupling. The calculated values of ${S}^{g}$ so obtained are in good agreement with those obtained for uncoupled wells. This confirms the experimental result that ${S}^{g}$ is insensitive to the resonance condition.