Floquet-driven tunneling control in monolayer MoS$_2$

We study how fermions in molybdenum disulfide MoS$_2$ interact with a laser field and a static potential barrier, focusing on the transmission probability. Our aim is to understand and control photon-assisted quantum transport in this two-dimensional material under external driving. We use the Floquet approximation to describe the wave functions in the three regions of the system. By applying continuity conditions at the boundaries, we obtain a set of equations involving an infinite number of Floquet modes. We explicitly determine transmissions involving the central band $E$ and the first sidebands $E \pm \hbar\omega$. As for higher-order bands, we use the transfer matrix approach together with current density to compute the associated transmissions. Our results reveal that the transmission probability oscillates for both spin-up and spin-down electrons. The oscillations of spin-down electrons occur over nearly twice the period of spin-up electrons. Among all bands, the central one consistently shows the highest transmission. We also find that stronger laser fields and wider barriers both lead to reduced transmission. Moreover, laser irradiation enables controllable channeling and filtering of transmission bands by tuning the laser intensity and system parameters. This highlights the potential of laser-driven MoS$_2$ structures for highly sensitive electromagnetic sensors and advanced optoelectronic devices.