Possible Wigner states in CrI3 heterostructures 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 a conduction band in a ferromagnetic $\mathrm{Cr}{X}_3$ monolayer, tuned to the complementary ab 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 neighbors, revealing ligand-mediated electron pathways connecting remote chromium sites. Doping of states in the lowest conduction band of $\mathrm{Cr}{X}_3$ requires charge transfer, which, according to recent studies [Tenasini et al., Nano Lett. 22, 6760 (2022); Tseng et al., Nano Lett. 22, 8495 (2022); Cardoso et al., Phys. Rev. B 108, 184423 (2023)], can occur in $\mathrm{graphene}\left(\mathrm{G}\right)/\mathrm{Cr}{X}_3$ heterostructures. Here, we use the detailed description of the lowest conduction band in ${\mathrm{CrI}}_3$ to show that $\mathrm{G}/{\mathrm{CrI}}_3/\mathrm{G}$ and $\mathrm{G}/{\mathrm{CrI}}_3$ are type-II heterostructures where light holes in graphene would coexist with heavy electrons in the magnetic layer, where the latter can be characterized by Wigner-Seitz radius $r_s\sim 25-35$ (as estimated for hBN-encapsulated structures).