Probing quantum geometry through optical conductivity and magnetic circular dichroism

Probing ground-state quantum geometry and topology through optical responses is not only of fundamental interest, but it can also offer several practical advantages. Here, using first-principles calculations on thin films of the antiferromagnetic topological insulator MnBi₂Te₄, we demonstrate how the generalized optical weight arising from the absorptive part of the optical conductivity can be used to probe the ground-state quantum geometry and topology. We show that three-septuple-layer MnBi₂Te₄ film exhibit an enhanced, almost-perfect magnetic circular dichroism for a narrow photon energy window in the infrared region. We calculate the quantum weight in this MnBi₂Te₄ film and show that it far exceeds the lower bound provided by the Chern number. Our results suggest that the well-known optical methods are powerful tools for probing the ground-state quantum geometry and topology.