Hall optical conductivity and Faraday rotation of monolayer transition metal dichalcogenides in the presence of proximity-induced exchange interaction and optical pumping

We present a detailed theoretical study on the optical conductivity and Faraday rotation of monolayer transition metal dichalcogenides (ML-TMDs) in the presence of proximity-induced exchange interaction introduced by a magnetic substrate, off-resonant light induced gap, a perpendicular electrical field, and a circularly polarized optical pumping. Taking monolayer molybdenum disulfide as an example, we develop a self-consistent quasi-equilibrium electronic system in the presence of circularly polarized optical pumping using the Boltzmann equation under the relaxation time approximation. The photoinduced carrier densities are evaluated by the corresponding rate equation, and the valley-resolved chemical potentials are determined self-consistently. The longitudinal and transverse (Hall) optical conductivities are calculated using the standard Kubo formula. It has been shown that the optical absorption, the optical Hall effect, and significant Faraday rotation angle can be effectively tuned by the proximity-induced exchange interaction, off-resonant light induced gap parameter, perpendicular electrical field, as well as the pumping photon energy and intensity. The results obtained suggest potential applications of optically modulated ML-TMD materials in optically tunable electronic and valleytronic devices.