Electron-electron interactions and the nonlinear Hall effect

Nonlinearities have become powerful diagnostics of a material’s symmetry and quantum geometry. A prime example is the nonlinear Hall effect that depend intricately on its Berry curvature distribution. These, however, have predominantly been explored in primarily non-interacting materials with the nonlinear Hall conductivities depending on single-particle band geometry. Here we discuss the role of electron-electron interactions in driving the nonlinear Hall effect as well as how interactions modify quantum geometry; we compare it with single particle counterparts that include the Berry curvature dipole (in time reversal symmetric materials) as well as the Berry connection polarizability induced intrinsic nonlinear Hall effect (in space-time symmetric antiferromagnets) providing means to understand the role of interactions in shaping the geometry of quantum matter.

*This work was supported by Singapore Ministry of Education (MOE) Academic Research Fund Tier 2 grant (MOE-T2EP50222-0011) and Tier 3 grant (MOE-MOET32023-0003) “Quantum Geometric Advantage”