Phonon-assisted magnetic Mott-insulating state in the charge density wave phase of single-layer 1TNbSe2

We study the structural, electronic and vibrational properties of single-layer 1TNbSe$_2$ from first principles. Within the generalized gradient approximation, the 1T polytype is highly unstable with respect to the 2H. The DFT+U method improves the stability of the 1T phase, explaining its detection in experiments. A charge density wave occurs with a $\sqrt{13}\times\sqrt{13}~R30^{\circ}$ periodicity, in agreement with STM data. At $U=0$, the David-star reconstruction displays a flat band below the Fermi level with a marked d$_{z^2-r^2}$ orbital character of the central Nb. The Hubbard interaction induces a magnetic Mott insulating state. Magnetism distorts the lattice around the central Nb atom in the star, reduces the hybridization between the central Nb d$_{z^2-r^2}$ orbital and the neighbouring Se p-states and lifts in energy the flat band becoming non-bonding. This cooperative lattice and magnetic effect amplifies the Mott gap. Single-layer 1TNbSe$_2$ is then a phonon-assisted spin-$1/2$ Magnetic Mott insulator.