Two-Gap Paring of the Optimal Doped (M,K)Fe$_{2}$As$_{2}$ with M = Ba, Sr

The gap structure revealed by the specific heat of iron pnictides remains unsettled. Not only do the reported characters vary for similar Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$ and Sr$_{0.55}$K$_{0.45}$Fe$_{2}$As$_{2}$, single gap and two-gap pairings have also been suggested in the crystals with the same nominal composition of Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$. It seems that either the gap structure is unusually sensitive to the sample details or some analysis procedures need to be refined Here we explored both the (Sr,K)Fe$_{2}$As$_{2}$ and (Ba,K)Fe$_{2}$As$_{2}$ systems, and different procedures were used to extract the phonon background. In the case of (Sr,K)Fe$_{2}$As$_{2}$, the phonon background seems to be insensitive to both the procedures and the potassium doping. For (Ba,K)Fe$_{2}$As$_{2}$, however, the data suggest a significant doping dependency of the soft phonons. The observations cast doubts on the previous procedures of using either BaFe$_{2}$As$_{2}$ or Ba(Fe$_{0.9}$Co$_{0.1})_{2}$As$_{2}$ to estimate the phonon background of Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$. A new procedure, therefore, is developed. The result will be presented and discussed.