Theory of thermopower in two-dimensional graphene

Abstract

Motivated by recent experiments by Yuri M. Zuev et al. [Phys. Rev. Lett. 102, 096807 (2009)], Peng Wei et al. [Phys. Rev. Lett. 102, 166808 (2009)], and Joseph G. Checkelsky et al. [Phys. Rev. B 80, 081413(R) (2009)], we calculate the thermopower of graphene incorporating the energy dependence of various transport scattering times. We find that scattering by screened charged impurities gives a reasonable explanation for the measured thermopower. The calculated thermopower behaves as $1/\sqrt{n}$ at high densities, but saturates at low densities. We also find that the thermopower scales with the normalized temperature $T/T_F$ and does not depend on the impurity densities, but strongly depends on the fine-structure constant $r_s$ and on the location of the impurities. We discuss the deviation from the Mott formula in graphene thermopower and use an effective-medium theory to calculate thermopower at low carrier density regimes where electron-hole puddles dominate.