Robust nonequilibrium edge currents with and without band topology

We study a two-dimensional lattice system 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. Using a nonperturbative approach, we characterize the nonequilibrium current distribution in different parameter regimes. 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. Interestingly, chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input.