Intrinsic nonlinear conductivities induced by the quantum metric

Three mechanisms are known to contribute to second-order nonlinear current: Extrinsic nonlinear Drude, Berry curvature dipole, and intrinsic Berry connection polarizability. Here, we predict an 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, this contribution is dissipative and contributes to both longitudinal and transverse 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.