Terahertz optical Hall effect in monolayer MoS2 in the presence of proximity-induced interactions

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The effect of proximity-induced interactions such as Rashba spin-orbit coupling (SOC) and exchange interaction on the electronic and optical properties of n-type monolayer (ML) ${\mathrm{MoS}}_{2}$ is investigated. We predict and demonstrate that the Rashba SOC can induce an in-plane spin splitting with terahertz (THz) energy, while the exchange interaction lifts the energy degeneracy in different valleys. Thus, spin polarization can be achieved in an n-type ML ${\mathrm{MoS}}_{2}$ and valley Hall or optical Hall effect can be observed using linearly polarized THz radiation. In such a case, the transverse optical conductivity ${\ensuremath{\sigma}}_{xy}(\ensuremath{\omega})$ results from spin-flip transition within spin-split conduction bands and from the fact that contributions from electrons with different spin orientations in different valleys can no longer be canceled out. Interestingly, we find that for fixed effective Zeeman field (or exchange interaction) the lowest spin-split conduction band in ML ${\mathrm{MoS}}_{2}$ can be tuned from one in the $K$ valley to another one in the ${K}^{\ensuremath{'}}$ valley by varying the Rashba parameter ${\ensuremath{\lambda}}_{R}$. Therefore, by changing ${\ensuremath{\lambda}}_{R}$ we can turn the sign of the spin polarization and $\mathrm{Im}{\ensuremath{\sigma}}_{xy}(\ensuremath{\omega})$ from positive to negative. Moreover, we find that the dominant contribution of the selection rules to ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ is from electrons in the $K$ valley and to ${\ensuremath{\sigma}}_{xy}(\ensuremath{\omega})$ is from electrons in the ${K}^{\ensuremath{'}}$ valley. These important and interesting theoretical findings can be helpful to experimental observation of the optical Hall effect in valleytronic systems using linearly polarized THz radiation fields.