Non-Hermitian quantum geometric tensor and nonlinear electrical response

Abstract: We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is a component of the QGT and takes complex values in non-Hermitian systems, generates an intrinsic nonlinear conductivity independent of the scattering time, while the complex Berry curvature induces a wavepacket-width-dependent response. Using one-dimensional and two-dimensional non-Hermitian models, we establish a universal link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena. Crucially, our analysis indicates that the wavepacket width significantly affects non-Hermitian transport -- a feature absent in Hermitian systems. This framework unifies non-Hermitian response theory by revealing how geometric degrees of freedom encode transport in open and synthetic quantum matter. Our results bridge fundamental quantum geometry with emergent functionality, offering pathways to exploit geometric effects in topological devices and engineered materials.