Monolayer-jacutingaite (Pt₂HgSe₃) has been predicted to be the first large-gap Kane-Mele quantum spin Hall insulator. Materials in the jacutingaite family undergo topological phase transitions (TPTs), i.e., from a topologically non-trivial to a semimetallic phase and further to the normal insulating phase when exposed to electric fields and off-resonance, high-frequency and high-intensity laser irradiation.

In this article, we investigate the rich tapestry of topological phases in this unique material in the presence of an appropriate choice of off-resonance circularly polarized laser fields and staggered sublattice potentials. The interplay of these stimuli with large spin-orbit coupling, due to the buckled structure of jacutingaite materials, results in the emergence of quantum spin Hall insulator, valley-spin-polarized metal, spin-polarized metal, photo-induced quantum Hall insulator, anomalous quantum Hall insulator and band insulator phases.

By analyzing the band structures, we compute Berry curvatures in different topological regimes for the K and K' valleys. Furthermore, by using the Kubo formula, we calculate the spin-valley resolved longitudinal and Hall conductivities as a function of photon energies, showing that the conductivities exhibit a strong topological-state dependence.