Derivative relations between electrical and thermoelectric quantum transport coefficients in graphene

TL;DR

This paper investigates the empirical relations between electrical and thermoelectric transport coefficients in graphene, confirming their validity across various conditions and exploring factors affecting their breakdown near the Dirac point.

Contribution

It demonstrates the robustness of these empirical relations in graphene and shows that the pre-factor remains unaffected by carrier density and mobility, except near the Dirac point.

Findings

Relations hold well in graphene except near the Dirac point.

Pre-factor _s is independent of carrier density and mobility.

Breakdown near the Dirac point may be due to carrier localization.

Abstract

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.