Superconducting order parameters with sign changes: The density of states and impurity scattering

Abstract

We compute ${\mathit{N}}_{\mathit{s}}$(E) for a family of superconducting order parameters with sign changes at the Fermi surface, and find surprising results. We consider all \ensuremath{\Delta}(k^) such that \ensuremath{\Delta}(k^)=+${\mathrm{\ensuremath{\Delta}}}_{0}$ on part of the Fermi surface, and \ensuremath{\Delta}(k^)=-${\mathrm{\ensuremath{\Delta}}}_{0}$ on the rest, yielding an average of 〈\ensuremath{\Delta}(k^)〉=r${\mathrm{\ensuremath{\Delta}}}_{0}$, where 0\ensuremath{\le}r\ensuremath{\le}1. For 0r1, as the impurity concentration increases, the number of low-lying states increases, and the superconductor becomes gapless. As the impurity concentration is further increased, the gap in the spectrum is restored, and ${\mathit{N}}_{\mathit{s}}$(E) approaches the pure limit BCS form, with a renormalized gap. \textcopyright{} 1996 The American Physical Society.