Nonequilibrium Exchange Nonlinear Hall Effect

Abstract

Quantum geometric electronic responses are often viewed through a non-interacting lens: independent quasiparticles accumulate Berry phases as they move through a static crystal and background potential. Here we argue that the combined action of electron-electron interactions and an out-of-equilibrium many-body state can produce striking departures from this familiar picture. We demonstrate how nonequilibrium exchange interactions produce a nonequilibrium collective quantum geometry distinct from that of its equilibrium ground state. We find this manifests as an exchange induced nonlinear Hall effect with nonlinear Hall current signals competitive with that of well-known non-interacting mechanisms. This highlights the critical role electron interactions and nonequilibrium states can play in the nonlinear response of quantum matter.