Superconductivity and impurity states in NbSe₂: An ab initio study

Superconductivity and charge-density wave (CDW) order are exotic low-temperature phenomena that coexist in certain layered two-dimensional transition metal dichalcogenides. The mechanism behind these competing, long-range, and collective electronic states has been extensively studied, however without much clarity of how their equilibrium can be destabilized by an external perturbation, such as chemical doping or pressure. In this work, ab initio calculations are first performed to identify the ground state CDW structure, and then the Migdal-Eliashberg theory, followed by the real-space Green's functions formalism, are employed to understand the superconducting properties as well as the effect of impurities in a monolayer NbSe₂. It is found that a small distortion in the Nb atoms stabilizes the lattice, forming a triangular Nb cluster in the CDW phase. Superconductivity is then suppressed due to the synergistic effect of the low density of states at the Fermi level and the low-frequency optical phonon hardening. The effect of impurities on the superconducting state is identified, and the results are ultimately analyzed in comparison with available experiments.