Triangular ad-atom surface lattices as a platform for correlated Hund's physics

In the triangular lattice Hubbard model, the interplay of strong correlations and geometrical frustration gives rise to a variety of emergent phenomena. At intermediate coupling a metal-insulator transition is observed and spin liquid physics have been proposed, whereas at strong coupling a magnetic insulator is found. Triangular lattice structures can be realized in a variety of materials, such as layered transition metal dichalcogenides, organic salts of the ?-ET family, or X:Si(111) ad-atom systems (X = Pb, Sn, C), where various kinds of correlated phenomena have been observed. In this work we propose X:SiC(0001) ad-atom systems (X = Cr, V, Ti) as a new platform to control and probe two-band physics in the triangular lattice Hubbard model. In particular we expect Hund's coupling to play a major role in the physics of V:SiC(0001). We use first-principles density functional theory calculations in conjunction with the constrained random phase approximation to derive a material-realistic model for the electronic structure. Using dynamical mean-field theory we explore the phase diagram as a function of ad-atom species and temperature.