Specific heat of Ba0.68K0.32Fe2As2: evidence for multiband strong-coupling superconductivity

The specific heat of high-purity $\mathrm{B}{\mathrm{a}}_{0.68}{\mathrm{K}}_{0.32}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ single crystals with the highest reported superconducting $T_c$ = 38.5 K was studied. The electronic specific heat, $C_p$, below $T_c$ shows two gap features, with ${\mathrm{\Delta }}_1\approx 11$ meV and ${\mathrm{\Delta }}_2\approx 3.5$ meV obtained from an $\alpha$-model analysis. The reduced gap value, $2\Delta^{\rm max} / k_B T_c \approx 6.6$,themagnitudeofthespecificheatjump,$\Delta C_p(T_c)/T_c$, and its slope below $T_c$ exhibit strong-coupling character. We also show that an Eliashberg model with two hole and two electron bands gives the correct values of $T_c$, the superconducting gaps, and the temperature dependence of the free-energy difference.