Power-law-like correlation between condensation energy and superconducting transition temperatures in iron pnictide/chalcogenide superconductors: Beyond the BCS understanding

Superconducting condensation energy $U_0^{int}$ has been determined by integrating the electronic entropy in various iron pnictide/chalcogenide superconducting systems. It is found that $U_0^{int}\propto T_c^n$ with $n$ = 3 to 4, which is in sharp contrast to the simple BCS prediction $U_0^{BCS}=1/2N_F\Delta_s^2$, with $N_F$ the quasiparticle density of states at the Fermi energy and $\Delta_s$ the superconducting gap. A similar correlation holds if we compute the condensation energy through $U_0^{cal}=3\gamma_n^{eff}\Delta_s^2/4\pi^2k_B^2$, with $\gamma_n^{eff}$ the effective normal state electronic specific heat coefficient. This indicates a general relationship $\gamma_n^{eff} \propto T_c^m$ with $m$ = 1 to 2, which is not predicted by the BCS scheme. A picture based on quantum criticality is proposed to explain this phenomenon.