Anomalous scaling of ΔC versus T_c in the Fe-based superconductors: the $S_{\pm }$-wave pairing state model

The strong power law behavior of the specific heat jump $\Delta C$ versus T _c $(\Delta C/T_c\sim T_c^{\alpha },\alpha \approx 2)$, first observed by Bud'ko et al (2009 Phys. Rev. B 79 220516), has been confirmed with several families of the Fe-based superconducting compounds with various dopings. We have tested a minimal two band BCS model to understand this anomalous behavior and showed that this non-BCS relation between $\Delta C$ versus T _c is a generic 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 $S_{\pm }$-wave pairing state. We also found that this $\Delta C$ versus T _c power law can continuously change from the ideal BNC scaling to a considerable deviation by a moderate variation of the impurity scattering rate ${\Gamma }_0$ (non-pair-breaking). As a result, our model provides a consistent explanation why the electron-doped Fe-based superconductors follow the ideal BNC scaling very well while the hole-doped systems often show varying degree of deviations. (paper)