Derivative relation for thermopower in the quantum Hall regime

Abstract

Recently, Tieke et al. [Phys. Rev. Lett. 78, 4621 (1997)] have observed the relation ${S}_{\mathrm{yx}}=\ensuremath{\alpha}{B(dS}_{\mathrm{xx}}/dB)$ for the components of the thermopower tensor in the quantum Hall regime, where \ensuremath{\alpha} is a constant and $B$ is the magnetic field. Simon and Halperin [Phys. Rev. Lett. 73, 3278 (1994)] have suggested that an analogous relation observed for the resistivity tensor ${R}_{\mathrm{xx}}=\ensuremath{\alpha}{B(dR}_{\mathrm{xy}}/dB)$ can be explained with a model of classical transport in an inhomogeneous medium where the local Hall resistivity is a function of position and the local dissipative resistivity is a small constant. In the present paper, we show that this thermopower relation can be explained with a similar model.