Intrinsic nonlinear conductivities induced by the quantum metric

The second-order nonlinear current originates from three physical mechanisms: extrinsic nonlinear Drude and Berry curvature dipole and intrinsic Berry connection polarizability. Here, we predict a new intrinsic contribution to the current related to the quantum metric, a quantum geometric property of the electronic wave function. This contribution manifests in systems that simultaneously break the time-reversal and the inversion symmetry. Interestingly, the new contribution is dissipative in nature and contributes to both longitudinal and the dissipative nonlinear Hall response. The quantum metric-induced NL current dominates transport in parity-time reversal symmetric systems near the band edges, something we show explicitly for topological antiferromagnets.