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., R x x and R x y ) and its counterpart between the Seebeck and Nernst coefficients (i.e., S x x and S x y ), 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, α s , does not depend on the carrier density in graphene. On tuning the carrier mobility and therefore the degree of disorder, 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.