Effect of Band Anisotropy on Phonon-Drag Thermopower in Alas Quantum Wells: Strong Enhancement of Phonon Drag

We present a detailed theoretical framework for the calculation of thermopower, S, in two-dimensional electron gases confined in (001) AlAs quantum wells (QWs) taking into account the band anisotropy. Particular emphasis is given on the phonon-drag contribution S-g that is related to the momentum exchange between acoustic phonons and electrons in the presence of a weak in-plane temperature gradient via the electron-phonon coupling. Our model is based on the semiclassical Boltzmann formalism and is a generalization of previous models that are applicable only for an isotropic energy spectrum. We find that the electron anisotropy in AlAs affects strongly the electron-acoustic phonon coupling and S-g. Considerable enhancement of S-g is reported in relation to isotropic GaAs QWs. More interestingly, we find that strong anisotropy in phonon-drag thermopower occurs by tuning the valley occupancy. Namely, the predicted S-xx(g) and S-yy(g) can differ by over a factor of 5 while a giant magnitude for S-g can be achieved in a particular direction exceeding 10 mV/K at T = 5 K. The diffusion thermopower is also calculated for comparison. DOI: 10.1103/PhysRevB.87.165304