1 \(\hbox {T}^{\prime }\) phase of the monolayer transition metal dichalcogenides has recently attracted attention for its potential in nanoelectronic applications. We theoretically prove the topological behavior and phase transition of 1 \(\hbox {T}^{\prime }\) - \(\hbox {MoS}_2\) using k.p Hamiltonian and linear response theory. The spin texture in momentum space reveals a strong spin-momentum locking with different orientations for the valence and conduction bands. Also, Berry curvature distributions around the Dirac points highlight the influence of \(\alpha\) parameter demonstrating a topological phase transition in 1 \(\hbox {T}^\prime\) - \(\hbox {MoS}_2\) . For \(\alpha <1\) the spin Hall conductivity is the only non-zero term \((C_s=1\) and \(C_v=0)\) , corresponding to a quantum spin Hall insulator (QSHI) phase, while for \(\alpha>1\) , valley Hall conductivity prevails, indicating a transition to a band insulator (BI). Further analysis explores the spin-valley-resolved Hall conductivity and Chern numbers across varying values of \(\alpha\) , V, and Fermi energy, uncovering regions of non-trivial and trivial topological phases (TTP) and the role of the edge modes. The zero total Nernst coefficient across energy ranges suggests strong cancellation between spin and valley contributions, providing insights into the material’s potential for thermoelectric applications and spintronic devices.
