Quantum Geometric Low-Frequency Optical Response of Correlated Metals

While single-particle electromagnetic responses of band insulators and semimetals are increasingly well-understood to interrogate geometrical and topological properties of Bloch states, optical signatures of quantum geometry in correlated electron systems remain a key open question. Here, we show that the low-frequency optical conductivity in correlated metals can directly probe the quantum geometry of the Fermi surface. This effect emerges from effective photon-dressed Coulomb scattering and can be equivalently understood to arise from light-induced perturbations of the band's Wannier functions. We illustrate ramifications for dilute-doped higher-angular-momentum topological band inversions in two dimensions with approximate Galilean invariance and show that the intraband optical conductivity due to electronic interactions becomes purely quantum-geometric in nature. Our results provide a new optical probe of quantum geometry in correlated electron systems.