Emerging spintronic and valleytronic phenomena in noncentrosymmetric variants of the Kane-Mele $X_4{Y}_2{Z}_6$ materials family ($X$ = Pt, Pd, Ni; $Y$ = Hg, Zn, Cd; $Z$ = S, Se, Te)

The realization of the Kane-Mele model in Xene solids faces challenges due to weak spin-orbit coupling (SOC). Nevertheless, the recently discovered $X_4{Y}_2{Z}_6$ family ($X$=Pt, Pd, Ni; $Y$=Hg, Zn, Cd; and $Z$=S, Se, Te) offers a promising opportunity with larger SOC. However, the presence of centrosymmetry in this family hinders the achievement of several cross-coupling phenomena based on spintronics and valleytronics. This study explores a noncentrosymmetric version of the Kane-Mele family, $X_{4}Y{Y}^{\prime }{Z}_6$ and $X_{4}Y{Y}^{\prime }{\left(Z{Z}^{\prime }\right)}_3$, comprising over 16 experimentally accessible members. The results reveal intertwined phenomena involving topology, spin, and valley degrees of freedom, including the quantum valley/spin Hall effect, spin-valley locking, and spin-valley selective optical transitions. Additionally, Rashba coupling coexists with Ising spin splitting, enabling valley spin valve functionality and out-of-plane spontaneous electric polarization. Quantum valley Hall kink states can be achieved on the domain walls between these noncentrosymmetric monolayers due to opposite spin-valley Berry curvatures. External factors, like electric fields and strain, induce various topological phase transitions. This study lays the foundation for exploring spin-valley physics in low-dimensional topological materials with noncentrosymmetry.