  We numerically study the general valley polarization and anomalous Hall
effect in van der Waals (vdW) heterostructures based on monolayer jacutingaite
family materials Pt$_{2}$AX$_{3}$ (A = Hg, Cd, Zn; X = S, Se, Te). We perform a
systematic study on the atomic, electronic, and topological properties of vdW
heterostructures composed of monolayer Pt$_{2}$AX$_{3}$ and two-dimensional
ferromagnetic insulators. We show that four kinds of vdW heterostructures
exhibit valley-polarized quantum anomalous Hall phase, i.e.,
Pt$_{2}$HgS$_{3}$/NiBr$_{2}$, Pt$_{2}$HgSe$_{3}$/CoBr$_{2}$,
Pt$_{2}$HgSe$_{3}$/NiBr$_{2}$, and Pt$_{2}$ZnS$_{3}$/CoBr$_{2}$, with a maximum
valley splitting of 134.2 meV in Pt$_{2}$HgSe$_{3}$/NiBr$_{2}$ and sizable
global band gap of 58.8 meV in Pt$_{2}$HgS$_{3}$/NiBr$_{2}$. Our findings
demonstrate an ideal platform to implement applications on topological
valleytronics.
