We propose three transition-metal adatom systems on SiC surfaces as a versatile platform to realize massless Dirac fermions and flat bands with strong electronic correlations. Using density functional theory combined with the constrained random phase approximation and dynamical mean-field theory, we investigate the electronic properties of Ti, V, and Cr adatoms. The triangular surface lattices exhibit narrow bandwidths and effective two-band Hubbard models near the Fermi level, originating from partially filled adatom $d$ orbitals. For the undoped systems our calculations reveal two distinct Mott insulating ground states. While the V lattice is a paramagnetic textbook case with large local moments, the Cr lattice, in contrast, is on the edge of a phase transition toward a flat-band Fermi liquid. The Ti lattice realizes a heavy Dirac semimetal at zero doping.

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• Flat bands
• Strongly correlated systems
• DFT+DMFT
• Electron-correlation calculations