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 $\Delta C\propto T_c^3$; for the penetration depth that deviates from the zero-$T$ value as $\Delta \lambda =\beta T^2$ at low temperatures with $\beta \propto T_c^{-3}$, and for the slopes of the upper critical fields $H_{c2}^{\prime }\left(T_c\right)\propto T_c$. A remarkably simple relation between these at first sight unrelated quantities is found: $\Delta C{\beta }^2{T}_c^4/\left|H_{c2}^{\prime }\right|={\varphi }_0/16{\pi }^2$ is a universal constant. The predictions are checked on ${\text{CeCoIn}}_5$ and the possibility to apply them to iron-based materials is discussed.

• Received 7 April 2010

DOI:https://doi.org/10.1103/PhysRevB.81.184528