Derivative relations between electrical and thermoelectric quantum transport coefficients in graphene

We find that the empirical relation between the longitudinal and Hall resistivities (i.e. Rxx and Rxy) and its counterpart between the Seebeck and Nernst coefficients (i.e. Sxx and Sxy), both originally discovered in two-dimensional electron gases, hold remarkably well for graphene in the quantum transport regime except near the Dirac point. The validity of the relations is cross-examined by independently varying the magnetic field and the carrier density in graphene. We demonstrate that the pre-factor, \alpha_s, does not depend on carrier density in graphene. By tuning the carrier mobility therefore the degree of disorders, we find that the pre-factor stays unchanged. Near the Dirac point, different mechanisms at low densities such as carrier localization may be responsible for the breakdown of these relations.