Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field

TL;DR

This paper analyzes the thermoelectric response of an interacting two-dimensional electron gas in a strong magnetic field, deriving expressions for currents and relating thermoelectric coefficients to thermodynamic quantities.

Contribution

It provides new theoretical expressions for bulk and boundary currents and links thermoelectric coefficients to equilibrium thermodynamic properties.

Findings

Transport currents obey Onsager relations.

Diffusion thermopower proportional to entropy per particle.

Boundary currents can carry significant net current.

Abstract

We present a discussion of the linear thermoelectric response of an interacting electron gas in a quantizing magnetic field. Boundary currents can carry a significant fraction of the net current passing through the system. We derive general expressions for the bulk and boundary components of the number and energy currents. We show that the local current density may be described in terms of ``transport'' and ``internal magnetization'' contributions. The latter carry no net current and are not observable in standard transport experiments. We show that although Onsager relations cannot be applied to the local current, they are valid for the transport currents and hence for the currents observed in standard transport experiments. We relate three of the four thermoelectric response coefficients of a disorder-free interacting two-dimensional electron gas to equilibrium thermodynamic quantities. In particular, we show that the diffusion thermopower is proportional to the entropy per particle, and we compare this result with recent experimental observations.