On the charge and magnetic ordering in monolayer NbSe${}_2$: a first principles study

Monolayer NbSe${}_2$ has recently been shown to be a 2-dimensional superconductor, with a competing charge-density wave (CDW) order. This work investigates the electronic structure of monolayer NbSe${}_2$ based on first principles calculations, focusing on charge and magnetic orders in connection to the superconductivity. It is found that decreased screening in the monolayer NbSe${}_2$ with a perfect lattice exhibits magnetic instability, which is removed by the formation of CDW. Two energetically competitive but distinct $3\times 3$ CDW structures are revealed computationally, which have a significant impact on the Fermi surface. The relations of the potential CDW phases with experimental structure and the coexisting superconductivity are discussed.