Floquet engineering of spin-valley selective transport in jacutingaite
We study electron transport through a monolayer jacutingaite (Pt$_2$HgSe$_3$) tunnel junction in which only the barrier is irradiated by off-resonant circularly polarized light, while the leads remain undriven. In the high-frequency regime, the driven barrier reduces to an effective static Dirac Hamiltonian with a photon-dressed, valley-dependent mass term. A staggered sublattice potential $V_z$ and a substrate-induced exchange field $m_s$ provide additional tunable mass terms. Using scattering theory, we compute spin- and valley-resolved transmission and reflection, as well as the Landauer conductance. Photon dressing shifts the barrier {Dirac masses} with opposite signs in the ($\boldsymbol{K}, \boldsymbol{K}'$) valleys and induces a splitting of the propagation thresholds. The finite barrier then produces channel-dependent Fabry--P\'erot-type interference through the phase $q_x^{\eta s_z}L$. We find broad parameter windows with near-perfect valley filtering ($|P_v|\simeq 100\%$) and substantial spin polarization ($|P_s|\sim 70\%$). The dominant spin and valley polarizations can be switched by tuning the drive amplitude $A_0$, $V_z$, and~$m_s$.