Frequency-dependent Faraday and Kerr rotation in anisotropic nonsymmorphic Dirac semimetals in a magnetic field*

We calculate the frequency-dependent longitudinal and Hall conductivities and the Faraday and Kerr rotation angles for a single sheet of anisotropic Dirac semimetal protected by nonsymmorphic symmetry in the presence of a magnetic field induces a gap in the band structure. While the magnetic field causes a rotation of the plane of polarization of the light, the anisotropy causes the appearance of an elliptically polarized component in an initially linearly polarized beam. The two effects can be combined in a single complex Faraday rotation angle. At the zero-frequency limit, we find a finite value of the Faraday rotation angle, which is given by 2αF, where αF is the effective fine structure constant associated with the velocity of the linearly dispersing Dirac fermions. We also find a logarithmic enhancement of the Faraday (and Kerr) rotation angles as the frequency of the light approaches the absorption edge associated with the magnetic field-induced gap. While the enhancement is reduced by impurity scattering, it remains significant for attainable levels of material purity. We provide general formulas expressing the polarizations of the transmitted and reflected light as a function of frequency for arbitrary initial polarizations and arbitrary directions of incidence. These results indicate that two-dimensional Dirac materials protected by non-symmorphic symmetry are responsive to weak magnetic fields and can be used as platforms for magneto-optic applications, such as the realization of polarization-rotating devices.