Quantum geometry probed by chiral excitonic optical response of Chern insulators

Quantum geometry describes phase and amplitude distances between quantum states, akin to Euclidean geometry in the classical world. The authors propose here probing the quantum geometry of Chern insulators via the excitonic optical response, using twisted bilayer MoTe${}_{2}$ as an example. In the terahertz frequency range, a single chiral exciton dominates the optical sum rule, enabling measurement of quantum geometry. This measurement could provide an assessment on the ideality of the quantum geometry, a key factor for realizing fractional Chern insulators.