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Graphene-based heterostructures are a promising material system for designingthe topologically nontrivial Chern insulating devices. Recently, atwo-dimensional (2D) monolayer ferromagnetic insulator CrI$_{3}$ wassuccessfully synthesized in experiments [Huang et al., Nature 546, 270 (2017)].Here, these two interesting materials are proposed to build a heterostructure(Gr/CrI$_{3}$). Our first-principles calculations show that the system forms avan der Waals (vdW) heterostructure, relatively facilely fabricated inexperiments. A Chern insulating state is acquired in the Gr/CrI$_{3}$heterostructure if the vdW gap is compressed to certain extents by applying anexternal pressure. Amazingly, very strong magnetization (about 150 meV) isfound in graphene, induced by the substrate CrI$_{3}$, despite the vdWinteractions between them. A low-energy effective model is employed tounderstand the mechanism. The work functions, contact types, and bandalignments of the Gr/CrI$_{3}$ heterostructure system are also studied. Ourwork demonstrates that the Gr/CrI$_{3}$ heterostructure is a promising systemto observe the quantum anomalous Hall effect at high temperatures (up to 45 K)in experiments.

Strong magnetization and Chern insulators in compressed graphene/CrI$_{3}$ van der Waals heterostructures