Fully nonequilibrium Hall response from Berry curvature

In topological materials, Berry curvature leads to intrinsic Hall responses. Focusing on time-reversal symmetric systems with broken inversion symmetry, a spontaneoous (zero magnetic field) Hall effect is expected to develop under an applied electric field. Motivated by recent developments in Weyl-Kondo semimetals, here we advance a fully nonequilibrium (FNE) Hall response due to the Berry curvature. In particular, we show that, while the spontaneous Hall current is quadratic in the previously described regime of weak electric field, due to the contribution from the dipole moment of the Berry curvature, the FNE Hall response for non-perturbative electric fields is not controlled by the Berry curvature dipole. Remarkably, the FNE Hall response resembles what happens in systems that break the microscopic time-reversal symmetry. We illustrate the universality of these results by comparing them with their counterparts in systems with any higher-multipole of the Berry curvature. The implications of our results for the understanding of strongly correlated topological semimetals are discussed.