Probing Quantum Geometry in Correlated Metals using Low-Frequency Optical Conductivity

Recent theoretical and experimental studies in Dirac and Weyl semimetals have revealed how the nontrivial quantum geometry of a band structure is embedded in its optical response. While most work has focused on the role of topology in interband excitations, here we examine the opposite limit where low-frequency light generates intraband excitations. We demonstrate that the terahertz optical conductivity of a metal encodes the structure of Bloch wave functions at the Fermi surface. Unlike for optical interband excitations, the role of electronic interactions is critical in this regime. We show that this response originates from integrating out highly off-resonant interband scattering processes and is the dominant contribution to the conductivity for a parabolic band proximate to a topological band inversion. Away from this limit, we show that, in addition to the well understood contributions from the dispersion relation, the optical conductivity of a correlated metal depends on the wave function geometry at the Fermi surface. Our results demonstrate that quantum geometry is a key ingredient in the physics of Fermi liquids and moreover provide a new route to probe quantum geometry in correlated systems through optical responses.