Effect of strong scattering on the low-temperature penetration depth of a<i>d</i>-wave superconductor

Abstract

For a pure superconductor in a d-wave-like state at temperatures T well below the critical temperature ${\mathit{T}}_{\mathit{c}}$, the deviation \ensuremath{\Delta}\ensuremath{\lambda} of the penetration depth from its zero-temperature value \ensuremath{\lambda}(0) is proportional to T. When the concentration ${\mathit{n}}_{\mathit{i}}$ of strongly scattering impurities is nonzero, \ensuremath{\Delta}\ensuremath{\lambda}\ensuremath{\propto}${\mathit{T}}^{\mathit{n}}$, where n=2 for T${\mathit{T}}^{\mathrm{*}}$\ensuremath{\ll}${\mathit{T}}_{\mathit{c}}$ and n=1 for ${\mathit{T}}^{\mathrm{*}}$T\ensuremath{\ll}${\mathit{T}}_{\mathit{c}}$. The crossover temperature ${\mathit{T}}^{\mathrm{*}}$ and the increase in \ensuremath{\lambda}(0) scale as \ensuremath{\surd}${\mathit{n}}_{\mathit{i}}$ up to logarithmic corrections when resonant scattering is dominant. We argue that this case is relevant to recent measurements on ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and present specific results for a model pairing state with ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry.