  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.
