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The quantum geometric properties of a Bloch state in momentum space areusually described by the Berry curvature and quantum metric. In realisticgapped materials where interactions and disorder render the Bloch state not aviable starting point, we generalize these concepts by introducing dressedBerry curvature and quantum metric at finite temperature, in which the effectof many-body interactions can be included perturbatively. These quantities areextracted from the charge polarization susceptibility caused by linearly orcircularly polarized electric fields, whose spectral functions can be measuredfrom momentum-resolved exciton or infrared absorption rate. As a concreteexample, we investigate Chern insulators in the presence of impurityscattering, whose results suggest that the quantum geometric properties areprotected by the energy gap against many-body interactions.

Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption