Anomalous scaling behavior of the Specific Heat jump $\Delta $C vs. T$_{\mathrm{c}}$ in the Fe-based superconductors

So called BNC scaling ($\Delta$C$\sim$T$_{\mathrm{c}}^{3}$) -- Bud'ko, Ni, and Canfield, PRB, 79, 220516 (2009)) -- has been observed in a wide range of the Fe-based superconducting compounds such as Ba(Fe$_{\mathrm{1-x}}$,Co$_{\mathrm{x}}$)$_{2}$As$_{2}$, Ba(Fe$_{\mathrm{1-x}}$,Ni$_{\mathrm{x}}$)$_{2}$As$_{2}$, BaFe$_{2}$(AsP)$_{2}$, and Ba$_{\mathrm{1-x}}$Na$_{\mathrm{x}}$Fe$_{2}$As$_{2}$. More recently, however, Canfield and coworkers reported that the Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$ compound severely deviates from this scaling when x\textgreater 0.7 and argued that this is an indication of the Lifshitz transition in the Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$ compound at higher hole-doping. In this presentation, we propose a theory that the BNC scaling as well as its strong deviation, as observed in Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$, are an intrinsic property of the multiband superconductor mediated by a dominant interband pairing potential as realized in the sign-changing S-wave state.