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. $T_c$ ($Delta C/T_c sim T_c ^{alpha}, alphaapprox 2$), first observed by Budko, 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.