Correlated Electron Effects in Chromium Trihalide Hetostructures with Graphene: A Tight-Binding Model Perspective

In this study, we present an effective tight-binding model for an accurate description of the lowest energy quadruplet of conduction band in a ferromagnetic CrX${}_3$ monolayer, tuned to the complementary $\mathit{\text{ab}}\mathit{\text{initio}}$ density functional theory simulations. This model, based on a minimum number of chromium orbitals, captures a distinctively flat dispersion in those bands but requires taking into account hoppings beyond nearest neighbours, revealing ligand-mediated electron pathways connecting remote chromium sites. Doping of states in the lowest conduction band of CrX${}_3$ requires charge transfer, which, according to recent studies, can occur in graphene(G)/CrX${}_3$ heterostructures. Here, we use the detailed description of the lowest conduction band in CrI${}_3$ to show that G/CrI${}_3$/G and G/CrI${}_3$ are type-II heterostructures where light holes in graphene would coexist with heavy electrons in the magnetic layer, where the latter can be characterised by Wigner parameter $r_s\sim 15-20$ (as estimated for hBN-encapsulated structures).