No bulk thermal currents in massive Dirac fermions

We calculate the energy current flowing in the bulk of a (2+1)-dimensional system of massive Dirac fermions and along a (1+1)-dimensional domain wall generated by flipping the sign of the particle mass. We show that, at low temperatures and in the long-wavelength limit, the system does not support a bulk thermal Hall current proportional to the temperature gradient. The only such contribution is due to states localized at the domain wall. This puts an end to a controversy existing in the literature and amends previous results obtained via first-order perturbation calculations. © 2024 authors. Published by the American Physical Society.