Nernst and Ettingshausen effects in gapped quantum materials

TL;DR

This paper explores the topological invariants related to thermoelectric effects in gapped 2D quantum materials, concluding that such invariants are limited to electric and thermal Hall conductances and that entropy-based invariants do not exist.

Contribution

It provides a comprehensive analysis showing the absence of thermoelectric topological invariants at zero temperature in gapped 2D materials, applicable to strongly interacting systems.

Findings

Thermoelectric transport coefficients vanish at zero temperature.

Topological invariants are limited to electric and thermal Hall conductances.

No entropy analog of the Thouless pump exists.

Abstract

We investigate whether there could exist topological invariants of gapped 2D materials related to dissipationless thermoelectric transport at low temperatures. We give both macroscopic and microscopic arguments showing that thermoelectric transport coefficients vanish in the limit of zero temperature and thus topological invariants arise only from the electric Hall conductance and the thermal Hall conductance. Our arguments apply to systems with arbitrarily strong interactions. We also show that there is no analog of the Thouless pump for entropy.