Robust non-equilibrium surface currents with and without band topology

We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. For both bosonic and fermionic systems, we find chiral edge currents that are robust against coupling to reservoirs and to the presence of defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. Therefore, an observer living on the boundary of the system sees very peculiar behaviour: the heat current locally flows from cold to hot, despite the second law of thermodynamics being obeyed overall. This novel boundary effect is found to persist in three-dimensional systems. We provide an explanation for the phenomenon in terms of the erasure effect --- currents in the bulk cancel while they add constructively on the boundary --- whose emergence is dictated by the nonequilibrium distribution function and the underlying symmetries of the lattice.