Quantum geometry induced third-order nonlinear transport responses

The authors develop here a comprehensive framework for third-order electronic transport, focusing on the impact of quantum geometry in materials where conventional responses are absent. By deriving new forms of reciprocal longitudinal and Hall currents in time-reversal symmetry-broken systems, they reveal how quantum geometric features -- specifically, the quantum geometric connection and tensor -- shape these nonlinear currents. This theoretical advancement provides a blueprint for identifying materials with intrinsic third-order responses, with potential applications in advanced quantum technologies.