Strong pairbreaking in anisotropic superconductors

Abstract

Abrikosov-Gor'kov work on pairbreaking in isotropic materials is generalized to anisotropic Fermi surfaces and order parameters. New scaling relations for states with a strong pairbreaking are found for the specific-heat jump $\ensuremath{\Delta}C\ensuremath{\propto}{T}_{c}^{3}$; for the penetration depth that deviates from the zero-$T$ value as $\ensuremath{\Delta}\ensuremath{\lambda}=\ensuremath{\beta}{T}^{2}$ at low temperatures with $\ensuremath{\beta}\ensuremath{\propto}{T}_{c}^{\ensuremath{-}3}$, and for the slopes of the upper critical fields ${H}_{c2}^{\ensuremath{'}}({T}_{c})\ensuremath{\propto}{T}_{c}$. A remarkably simple relation between these at first sight unrelated quantities is found: $\ensuremath{\Delta}C{\ensuremath{\beta}}^{2}{T}_{c}^{4}/|{H}_{c2}^{\ensuremath{'}}|={\ensuremath{\phi}}_{0}/16{\ensuremath{\pi}}^{2}$ is a universal constant. The predictions are checked on ${\text{CeCoIn}}_{5}$ and the possibility to apply them to iron-based materials is discussed.