Gapless Superconductivity From Extremely Dilute Magnetic Disorder in 2H‐NbSe _{2‐ <i>x</i>} S _<i>x</i>

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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>NbSe</mml:mi> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>-</mml:mo> <mml:mi>x</mml:mi></mml:mrow> </mml:msub> <mml:mi>S</mml:mi></mml:mrow> <mml:annotation>${\rm NbSe}_{2-x}{\rm S}$</mml:annotation></mml:semantics> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mrow></mml:mrow> <mml:mi>x</mml:mi></mml:msub> <mml:annotation>$_x$</mml:annotation></mml:semantics> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>x</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn></mml:mrow> <mml:annotation>$x>0$</mml:annotation></mml:semantics> </mml:math> , in stark contrast to the dominant charge density wave interactions in pure 2H- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>NbSe</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:annotation>${\rm NbSe}_2$</mml:annotation></mml:semantics> </mml:math> . 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.