Nb$_3$Cl$_8$: A Prototypical Layered Mott-Hubbard Insulator

The Hubbard model provides an idealized description of electronic correlations in solids. Despite its simplicity, the model features a competition between several different phases that have made it one of the most studied systems in theoretical physics. Real materials usually deviate from the ideal of the Hubbard model in several ways, but the monolayer of Nb$_3$Cl$_8$ has recently appeared as a potentially optimal candidate for the realization of such a single-orbital Hubbard model. Here we show how this single orbital Hubbard model can be indeed constructed within a "molecular" rather than atomic basis set using ab initio constrained random phase approximation calculations. This way, we provide the essential ingredients to connect experimental reality with ab initio material descriptions and correlated electron theory, which clarifies that monolayer Nb$_3$Cl$_8$ is a Mott insulator with a gap of about 1 to 1.2eV depending on its dielectric environment. By comparing with an atomistic three-orbital model, we show that the single molecular orbital description is indeed adequate. We furthermore comment on the expected electronic and magnetic structure of the compound and show that the Mott insulating state survives in the low-temperature and bulk phases of the material.