  The effect of electron-phonon scattering processes over the thermoelectric
properties of extrinsic graphene was studied. Electrical and thermal
resistivity, as well as the thermopower, were calculated within the Bloch
theory approximations. Analytical expressions for the different transport
coefficients were obtained from a variational solution of the Boltzmann
equation. The phonon-limited electrical resistivity \rho_{e-ph} shows a linear
dependence at high temperatures, and follows {\rho}_{e-ph} \sim T^{4} at low
temperatures, in agreement with experiments and theory previously reported in
the literature. The phonon-limited thermal resistivity at low temperatures
exhibits a \sim T dependence, and achieves a nearly constant value at high
temperatures. The predicted Seebeck coefficient at verylow temperatures is Q(T)
\sim -\pi 2 k_B T /(3 e E_F), which shows a n^{-1/2} dependence with the
density of carriers, in agreement with experimental evidence. Our results
suggest that thermoelectric properties can be controlled by adjusting the
Bloch-Gruneisen temperature through its dependence on the extrinsic carrier
density in graphene.

Mesoscale and Nanoscale Physics;Statistical Mechanics