Probing Doped Two-Dimensional Mott Insulators with Graphene

We discuss the properties of the class of two-dimensional materials formed by stacking graphene and two-dimensional Mott insulators like CrI₃ and RuCl₃. The coupling between layers is normally weak in these systems, allowing the electrical transport of the graphene layers to be used as a weak probe of the Mott insulators. Because of large differences in chemical potential between layers, both graphene and Mott insulator layers are normally doped. We will discuss how capacitance measurements in dual-gated stacks allow to probe thermodynamic properties of the Mott insulator layers and their dependence on magnetic state, whether ferromagnetic, antiferromagnetic, or spin liquid. We will also address the nature of the coupling between the two materials and its dependence on lattice constant differences, which are normally large, relative orientation, and the magnetic configuration of the insulator using a Hartree-Fock mean-field theory description of the doped Mott insulators.