  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.
