Quantum geometry in a flat band kagome metal

The spectrum of flat band materials in condensed matter physics has recently expanded with the realization of geometry-driven flat bands in kagome and pyrochlore lattices. Unlike trivial atomic flat bands, these geometry-driven flat bands exhibit nontrivial quantum geometry, promising the realization of novel flat band phenomena, including fractional quantum Hall effect, anomalous Landau level spreading, and flat band superfluidity. In this work, we develop a framework to extract the full quantum geometric information in solids using polarization-, spin-, and angle-resolved photoemission spectroscopy, and provide experimental measurements of the quantum metric and Berry curvature in the archetypal kagome metal CoSn hosting geometry-driven flat bands. The key idea is to introduce another geometric quantity, the band Drude weight and orbital angular momentum, which are experimentally accessible and approximate the quantum metric and Berry curvature in the two-band limit. Our work establishes a momentum- and energy-resolved spectroscopic probe of quantum geometric information in solids, poised to significantly advance our understanding of rich geometric responses in quantum materials.