Maximization of Thermopower in Optimally-Disordered Graphene

We study the interplay of electron-phonon and electron-impurity scattering in graphene and its manifestations in thermopower S. Electron scattering by acoustic phonons dominating in clean samples results in energy-independent carrier diffusivity, which translates into zero value of S. Inclusion of charged impurities plays a twofold role. At low impurity densities, the diffusivity becomes energy-dependent, which elevates S. In largely disordered samples, the carrier density becomes inhomogeneous, which results in self-averaging of thermopower. The latter effect is tackled here with effective medium theory, and predicts a slow drop in S with increasing the impurity density. The competition of these effects results in thermopower maximization at an optimal density of impurities nimp. The latter is estimated as 2 × 1011 cm–2 at room temperature, which corresponds to the highest-quality chemical vapor deposited graphene.