Supplementary Material

In this Supplementary Material, we provide detailed computational methods of computational methods include first-principles calculations, phonon thermal conductivity and unified theory, the convergence tests of q-point meshes, the description of electronic structure, lattice thermal conductivity of intrinsic monolayer MoS$_2$, the lattice parameters, bond length for monolayer MoS$_2$ and WS$_2$ in NS and two-SFs structures, the band structures with/without SOC, 3D band structures, electron localization function (ELF) map, the \textit{ab initio} molecular dynamics (AIMD) simulationsand cumulative $\kappa_L$ with respect to the phonon frequency of two-SFs MoS$_2$ and two-SFs WS$_2$. The phonon group velocities, specific heat, and cumulative $\kappa_L$ of intrinsic MoS$_2$ and two-SFs MoS$_2$.