Probing quantum geometry through optical conductivity and magnetic circular dichroism

In a crystalline solid, the quantum metric and the Berry curvature together constitute the complex quantum geometry of the ground state wavefunction. Optical responses, however, are mostly related to photon-assisted interband transitions. Thus, probing ground state quantum geometry through optical response is highly interesting and can offer several practical advantages. Here, using density functional theory-based first-principles calculations and by taking antiferromagnetic topological insulator MnBi2Te4 thin films as example materials, we show that generalized optical weight arising from the first negative moment of the absorptive part of the optical conductivity can be used to probe the ground state quantum geometry. We estimate the Faraday and Kerr rotation angles and magnetic circular dichroism in the odd septuple layer MnBi2Te4. Our results suggest that the well-known optical methods can be used to probe the ground state quantum geometry.