Circular dichroism and Faraday and Kerr rotation in two-dimensional materials with intrinsic Hall conductivities

The electronic structures of two-dimensional hexagonal materials for a given spin direction can be generally written by the Haldane model, which shows circular dichroism or valley polarization due to broken time-reversal and inversion symmetries, respectively. By using the Kubo formula, we calculate longitudinal and transversal (Hall) optical conductivities to obtain the absorption spectra. The absorption spectra for circularly polarized lights are calculated by solving the Maxwell equations with a boundary conditions at the two-dimensional material. We found that circular dichroism and valley polarization depend on the properties of the imaginary part of the Hall conductivity, while the real part of the Hall conductivity generates large Faraday and Kerr rotations up to a few degrees.