Disorder Effects in Superconductors with Anisotropic Pairing: From Cooper Pairs to Compact Bosons

In the weak coupling BCS-approximation normal impurities do not influence superconducting T_{c} in significant manner in case of isotropic s-wave pairing. However, in case of d-wave pairing these are strongly pair-breaking. This fact is in rather strong contradiction with many experiments on disordered high-T_{c} superconductors assuming the d-wave nature of pairing in these systems. With the growth of electron attraction within the Cooper pair the system smoothly crosses over from BCS-pairs to compact Boson picture of superconductivity. As pairing strength grows and pairs become compact significant deviations from universal Abrikosov-Gorkov dependence of T_{c} on disorder appear in case of d-wave pairing with superconducting state becoming more stable than in the weak coupling case. As high-T_{c} superconductors are actually in the intermediate region with Cooper pairs size of the order of few interatomic lengths, these results can explain the relative stability of d-wave pairing under rather strong disordering.

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