Quantum geometry in low-energy linear and nonlinear optical responses of the magnetic Rashba semiconductor (Ge,Mn)Te

Quantum geometry appears as a key factor in understanding the optical properties of quantum materials, with the anticipation on diverging or quantized responses near the Dirac and Weyl points. Here we investigate linear and nonlinear optical responses -- optical conductivity and injection current -- in a magnetic Rashba semiconductor in the mid-infrared region, with varying the Fermi energy across the Dirac point. We reveal that the linear optical conductivity reflects quantum metric, which remains finite irrespective of the diminishing joint density-of-states at lower photon energy. It is also confirmed that the magnetic injection current enhances depending on the energy of the Fermi level relative to the Dirac point. These optical spectra are nicely reproduced by our theoretical calculations with geometrical effects taken into account.