Derivative relation for thermopower in the quantum Hall regime

TL;DR

This paper explains a recently observed relation between thermopower tensor components in the quantum Hall regime using a classical inhomogeneous medium model, extending previous resistivity tensor relations.

Contribution

It demonstrates that the thermopower relation S_{yx} = alpha B dS_{xx}/dB can be derived from a classical inhomogeneous medium model, similar to earlier resistivity relations.

Findings

The thermopower relation is consistent with a classical inhomogeneous medium model.

The model explains the observed relation without invoking quantum effects.

It extends the classical transport explanation to thermopower tensor components.

Abstract

Recently, Tieke et al (to be published in PRL) have observed the relation S_{yx} = alpha B dS_{xx}/dB for the components of the thermopower tensor in the quantum Hall regime, where alpha is a constant and B is the magnetic field. Simon and Halperin (PRL 73, 3278 (1994)) have suggested that an analogous relation observed for the resistivity tensor R_{xx} = \alpha B dR_{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 new thermopower relation can be explained with a similar model.