Origin and properties of the flat band in monolayer NbOCl2

The existence of a flat band near the Fermi level can be a suitable platform for the emergence of interesting phenomena in condensed matter physics. Recently, ${\mathrm{NbOCl}}_{2}$ monolayer has been experimentally synthesized [Q. Guo et al., Nature (London) 613, 53 (2023)], which has a flat and isolated valence band. Motivated by the recent experiment, we investigate the origin of the flat band as well as the electronic, optical, photocatalytic, and magnetic properties of the monolayer by combining density functional theory and many-body quantum perturbation theory. Our results show that the flat and isolated band of this monolayer is caused by the interplay between the Peierls distortion and the electronic configuration of Nb atoms. We show that monolayers based on other elements of group 5 of the periodic table, including the V and Ta atoms, also have a flat band. The investigation of the bandwidth of the monolayer under the biaxial and uniaxial strains reveals that this material can be grown on substrates with a larger lattice constant by maintaining the flat band. Examining the material's response to the linearly polarized light not only reveals the presence of weak optical anisotropy, but also shows the existence of a bright exciton with a binding energy of about 0.94 eV. Hole doping can result in a flat-band-induced phase transition from semiconductor to ferromagnet. By adjusting the amount of doping, a bipolar magnetic semiconductor or a half metal can be created. The interaction between the nearest Nb atoms is ferromagnetic, while an antiferromagnetic interaction appears between the second neighbors, which grows significantly with increasing doping. Our results demonstrate that ${\mathrm{NbOCl}}_{2}$ monolayer has a suitable potential for spintronic applications in addition to electronic and optoelectronic applications.