Probing quantum geometry through optical conductivity and magnetic circular dichroism

Probing ground-state quantum geometry and topology through optical response is not only of fundamental interest, but it can also offer several practical advantages. Here, using first-principles calculations on antiferromagnetic topological insulator MnBi$_2$Te$_4$ thin films, 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 layers MnBi$_2$Te$_4$ exhibit an enhanced almost perfect magnetic circular dichroism for a narrow photon energy window in the infrared region. We calculate the quantum weight in a few septuple layers MnBi$_2$Te$_4$ 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.