Effects of a piezoelectric substrate on phonon-drag thermopower in monolayer graphene

Abstract

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 ns. 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 μm size, we predict S g ~ 20 μV 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 ns 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 ~ ns -1/2 . The T (ns ) 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 μp ~ T -1 ), we predict a new relation S g μp ~ ns 0 , where μp is the phonon-limited mobility. We suggest that ns-dependent measurements will play a more significant role in identifying the Dirac phase and the effect of screening.