  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.
