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Thermopower of multilayer graphene

We systematically calculate thermopower of biased and unbiased multilayer grphene systems. The effect of screening to a bias field perpendicular to the graphene planes is taken into account self-consistently under the Hartree approximation. The model including nearest neighbor hopping and the more complete Slonczewski-Weiss-McClure (SWMcC) model are both considered for a comparison. The effect of impurity scattering is studied for monolayer and unbiased bilayer graphene and is treated in terms of the self-consistent Born approximation. For a monolayer graphene, only when the effect of impurity scattering is taken into account, could all the qualitative aspects of the experimental results be correctly reproduced. A small energy gap opens for the biased trilayer graphene. When the carrier density is high enough, a gap is also found for unbiased trilayer and quad-layer graphene. The biased bilayer graphene shows the largest thermopower among all the systems studied.