Magnetic field dependent two-photon absorption properties in monolayer MoS2

We report our theoretical investigations on the magnetic field dependence of two-photon absorption (TPA) properties in ${\mathrm{MoS}}_{2}$. Based on the Landau levels obtained by the effective massive Dirac model, we developed TPA theories associated with both interband transitions and intraband transitions for transitional metal dichalcogenides (TMDCs) with a magnetic field under the second-order perturbation theory with respect to the electron-photon interaction. Our results reveal that the TPA coefficient is effectively enhanced by five orders of magnitude under the application of an external magnetic field, which results in the quantized horizontal Landau levels with the spin-orbit coupling (SOC) and valley Zeeman effects. The TPA peaks are located in the terahertz regime for intraband transitions and in the visible regime for interband transitions. The amplitude of TPA contributed by intraband transitions is much larger than that of interband transitions owing to the resonant transitions. Oscillatory behavior appeared in the interband transition-related TPA spectra. The separation of TPA for the transitions in the spin-up and spin-down states caused by the spin splitting of Landau levels resulting from the strong SOC is illustrated. We also analyzed the anisotropy of TPA associated with the direction of the incident light. Our results are of much importance for the application of TMDCs in optical devices.