Nernst and Ettingshausen effects in gapped quantum materials

We investigate whether there could exist topological invariants of gapped two-dimensional 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.