We present a theoretical framework to investigate quantum magnetotransport in monolayer jacutingaite, focusing on its response to external electric fields and off-resonant circularly polarized laser irradiation. Our analysis reveals a sequence of topological phase transitions triggered by tuning these external parameters. Applying a perpendicular magnetic field, we study Landau level (LL) formation, spin- and valley-polarized splitting, and magneto-optical response in distinct topological phases. We find that the zeroth LL exhibits spin- and valley-polarized splitting, leading to four distinct peaks in the DOSs for the $K$ and $K^{\prime }$ valleys. We demonstrate that reversing the electric field or flipping the light helicity changes the Dirac mass sign in specific spin-valley sectors, which in turn reverses both the Berry curvature and the magnetic moment. Our results reveal that external electric, magnetic, and off-resonant optical fields can control these conductivities. These findings highlight monolayer jacutingaite as a highly tunable platform with strong potential for future applications in photonics, optoelectronics, and topological quantum devices.

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• Electrical properties
• Geometric & topological phases
• Optical conductivity
• Spin-orbit coupling
• Topological insulators
• Topological phases of matter
• Transport phenomena
• Valley degrees of freedom