Quantized optical conductivity of gated and irradiated monolayer Pt$_2$HgSe$_3$

This study explores the optical conductivity of monolayer jacutingaite (Pt2HgSe3) under tunable gap parameters induced by both static and dynamic electric fields, focusing on interband and intraband transitions. We analyze the photon energy dependence of the optical response, revealing distinct features: the intraband contribution displays a characteristic Drude-like decay, while the interband response exhibits a sharp onset at a threshold energy, consistent with the presence of an energy gap and underlying phase structure. While the pristine Hall conductivity is negligible, it is significantly enhanced through inversion and time-reversal symmetry breaking, achieved via static and dynamic electric fields, respectively. By tuning the gap parameter, we demonstrate a shift in the onset of interband transitions toward lower and higher photon energies, signaling various topological phase transitions. Our findings highlight the material's tunable optical response, with implications for spintronic and valleytronic applications, and underscore the critical role of the energy gap in governing optical absorption and topological characteristics.