Effect of piezoelectric substrate on phonon-drag thermopower in monolayer graphene

The phonon-drag thermopower is studied in monolayer graphene on a piezoelectric substrate. The phonon-drag contribution S^g_PA from the extrinsic potential of piezoelectric surface acoustic (PA) phonons of a piezoelectric substrate (GaAs) is calculated as a function of temperature T and electron concentration n_s. At very low temperature, S^g_PA is found to be much greater than S^g_DA of the intrinsic deformation potential of acoustic (DA) phonons of the graphene. There is a crossover of S^g_PA and S^g_DA at around ~5 K. In graphene samples of about >10 um size, we predict S_g ~20 uV at 10 K, which is much greater than the diffusion component of the thermopower and can be experimentally observed. In the Bloch-Gruneisen (BG) regime T and n_s dependence are, respectively, given by the power laws S^g_PA (S^g_DA) ~ T^2(T^3) and S^g_PA, S^g_DA ~ n_s^(-1/2). The T (n_s) dependence is the manifestation of the two-dimensional phonons (Dirac phase of the electrons). The effect of the screening is discussed. Analogous to Herring's law (S_g mu_p ~T^-1), we predict a new relation S_g mu_p ~n_s^0, where mu_p is the phonon-limited mobility. We suggest that n_s dependent measurements will play a more significant role in identifying the Dirac phase and the effect of screening.