Gapless Superconductivity From Extremely Dilute Magnetic Disorder in 2H-NbSe_2-xS_x

Most superconducting materials exhibit a vanishing density of states at the Fermi level and Anderson's theorem posits that the superconducting gap is robust against nonmagnetic disorder. Although dilute magnetic impurities lead to localized in-gap states, these states typically have no bearing on the material's bulk superconducting properties. However, numerous experiments reveal a finite density of states at the Fermi level in systems with an apparently negligible number of magnetic impurities. Here, using scanning tunneling microscopy and self-consistent Bogoliubov-de Gennes calculations, we find that gapless superconductivity emerges in 2H- ${\mathrm{NbSe}}_{2-x}S$ ${}_x$ at remarkably low magnetic impurity concentrations. Furthermore, our density functional theory calculations and in-gap quasiparticle interference measurements demonstrate that the Se-S substitution significantly modifies the band structure. This modification favours nesting and dictates the in-gap scattering for $x>0$ , in stark contrast to the dominant charge density wave interactions in pure 2H- ${\mathrm{NbSe}}_2$ . Our findings reveal an unusual superconducting response to disorder and highlight the importance of incorporating material-specific band structures in the understanding of a superconductor's response to even very low concentrations of magnetic impurities.