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We identify a valley-polarized Chern insulator in the van der Waalsheterostructure, Pt$_{2}$HgSe$_{3}$/CrI$_3$, for potential applications withinterplay between electric, magnetic, optical, and mechanical effects. Theinterlayer proximity magnetic coupling nearly closes the band gap ofPt$_{2}$HgSe$_{3}$ and the strong intra-layer spin-orbit coupling further liftsthe valley degeneracy by over 100 meV leading to positive and negative bandgaps at opposite valleys. In the valley with negative gap, the interfacialRashba spin-orbit coupling opens a topological band gap of 17.8 meV, which isenlarged to 30.8 meV by adding an $h$-BN layer. We find large orbitalmagnetization in Pt$_{2}$HgSe$_{3}$ layer that is much larger than spin, whichcan induce measurable optical Kerr effect. The valley polarization and Chernnumber are coupled to the magnetic order of the nearest neighboring CrI$_3$layer, which is switchable by electric, magnetic, and mechanical means inexperiments. The presence of $h$-BN protects the topological phase allowing theconstruction of superlattices with valley, spin, and layer degrees of freedoms.

Van der Waals Heterostructure Pt$_{2}$HgSe$_{3}$/CrI$_3$ for Topological Valleytronics