Anomalous scaling of the specific-heat jump $\Delta C$ vs. $T_c$ in the Fe-based superconductors: the $\pm$S-wave pairing state model
The strong power law behavior of the specific heat jump $\Delta C$ vs. $T_c$ ($\Delta C/T_c \sim T_c ^{\alpha}, \alpha\approx 2$), first observed by Bud'ko, Ni, and Canfield (BNC)[1], has been confirmed with several families of the Fe-based superconducting compounds with a series of doping. We show here that this anomalous non-BCS behavior is an intrinsic property of the multiband superconducting state paired by a dominant interband interaction ($V_{inter} > V_{intra}$) reflecting the relation $\frac{\Delta_h}{\Delta_e} \sim \sqrt{\frac{N_e}{N_h}}$ near $T_c$, as in the $\pm$S-wave pairing state. Then this $\Delta C$ vs. $T_c$ relation can continuously change from the perfect BNC scaling to a considerable deviation at lower $T_c$ region with a moderate variation of the impurity scattering rate.