  Semiconductor surfaces with narrow surface bands provide unique playgrounds
to search for Mott-insulating state. Recently, a combined experimental and
theoretical study [Phys. Rev. Lett. 114, 247602 (2015)] of the two-dimensional
(2D) Sn atom lattice on a wide-gap SiC(0001) substrate proposed a Mott-type
insulator driven by strong on-site Coulomb repulsion U. Our systematic
density-functional theory (DFT) study with local, semilocal, and hybrid
exchange-correlation functionals shows that the Sn dangling-bond state largely
hybridizes with the substrate Si 3p and C 2p states to split into three surface
bands due to the crystal field. Such a hybridization gives rise to the
stabilization of the antiferromagnetic order via superexchange interactions.
The band gap and the density of states predicted by the hybrid DFT calculation
agree well with photoemission data. Our findings not only suggest that the
Sn/SiC(0001) system can be represented as a Slater-type insulator driven by
long-range magnetism, but also have an implication that taking into account
long-range interactions beyond the on-site interaction would be of importance
for properly describing the insulating nature of Sn/SiC(0001).
