arXiv2026
We investigate the systematic competition between perpendicular electric field and circularly polarized light in nonequilibrium topological phases of monolayer 1T$^\prime$--MoS$_2$ using a low-energy $k\!\cdot\!p$ Hamiltonian and Floquet theory. The off-resonant field generates spin- and valley-dependent mass corrections that reshape the Berry curvature (BC) and shift the conditions for band inversion. By evaluating the quasienergy bands, BC, and spin- valley-resolved Chern numbers, we identify a sequence of light and electric field controlled topological transitions by gap closing. Depending on the Floquet coupling strength and the electric-field parameter, the system evolves between the equilibrium quantum spin Hall (QSH) state and a set of driven phases including spin-polarized quantum Hall insulator (S-QHI), band insulator (BI) and photo-induced quantum Hall insulator (P-QHI) regimes. The results establish 1T$^\prime$--MoS$_2$ as a tunable platform where circular driving selectively manipulates spin and valley degrees of freedom, enabling controlled access to non-equilibrium topological phases in transition metal dichalcogenides (TMDs).