$\textit{Ab Initio}$ Mismatched Interface Theory of Graphene on $\alpha$-RuCl$_3$: Doping and Magnetism

Recent developments in twisted and lattice-mismatched bilayers have revealed a rich phase space of van der Waals systems and generated excitement. Among these systems are heterobilayers which can offer new opportunities to control van der Waals systems with strong in plane correlations such as spin-orbit-assisted Mott insulator $\alpha$-RuCl$_3$. Nevertheless, a theoretical $\textit{ab initio}$ framework for mismatched heterobilayers without even approximate periodicity is sorely lacking. We propose a general strategy for calculating electronic properties of such systems, mismatched interface theory (MINT), and apply it to the graphene/$\alpha$-RuCl$_{3}$ (GR/$\alpha$-RuCl$_{3}$) heterostructure. Using MINT, we predict uniform doping of 4.77$\%$ from graphene to $\alpha$-RuCl$_3$ and magnetic interactions in $\alpha$-RuCl$_3$ to shift the system toward the Kitaev point. Hence we demonstrate that MINT can guide targeted materialization of desired model systems and discuss recent experiments on GR/$\alpha$-RuCl$_{3}$ heterostructures.