Thermopower of a double quantum well based on GaAs

The resistivity and thermopower of a double quantum well have been investigated in the temperature range $0.3-4.2\mathrm{K}$ 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.