Low-energy quasiparticle states near extended scatterers in d-wave superconductors and their connection with SUSY quantum mechanics

Low-energy quasiparticle states, arising from scattering by single-particle potentials in d-wave superconductors, are addressed. Via a natural extensi on of,the Andreev approximation, the idea that sign variations in the super conducting pair potential lead to such states is extended beyond its origin al setting of boundary scattering to the broader context of scattering by g eneral single-particle potentials, such as those due to impurities. The ind ex-theoretic origin of these states is exhibited via a simple connection wi th Witten's supersymmetric quantum-mechanical model.