Electronic structure of single layer 1T-NbSe: interplay of lattice distortions, non-local exchange, and Mott-Hubbard correlations.

Using ab initio calculations we reveal the nature of the insulating phase recently found experimentally in monolayer 1T-NbSe. We find soft phonon modes in a large part of the Brillouin zone indicating the strong-coupling nature of a charge-density-wave instability. Structural relaxation of a [Formula: see text] supercell reveals a Star-of-David reconstruction with an energy gain of 60 meV per primitive unit cell. The band structure of the distorted phase exhibits a half-filled flat band which is associated with orbitals that are delocalized over several atoms in each Star of David. By including many-body corrections through a combined GW, hybrid-functional, and DMFT treatment, we find the flat band to split into narrow Hubbard bands. The lowest energy excitation across the gap turns out to be between itinerant Se-p states and the upper Hubbard band, determining the system to be a charge-transfer insulator. Combined hybrid-functional and GW calculations show that long-range interactions shift the Se-p states to lower energies. Thus, a delicate interplay of local and long-range correlations determines the gap nature and its size in this distorted phase of the monolayer 1T-NbSe.