Superconducting gap structure in over-doped (Ba$_{1-x}$,K$_x$)Fe$_2$As$_2$ ($x=$0.35, 0.47, 0.56, and 0.64) from London penetration depth measurements

Single crystals of (Ba$_{1-x}$,K$_x$)Fe$_2$As$_2$ were extensively studied from the optimal doping to the very underdoped regime. However, overdoped regime was out of reach due to various issues with the crystal growth. Here we report London penetration depth measured in high quality single crystals of (Ba$_{1-x}$,K$_x$)Fe$_2$As$_2$ with ($x=$0.35, 0.47, 0.56, and 0.64) that have $T_c=$30 K, 39 K, 32 K and 22 K, respectively. The study of the evolution from the optimally doped composition toward the end member, KFe$_2$As$_2$, is especially important, since the former is clearly a full isotropic gap material, whereas the latter is a d-wave superconductor. Our results suggest a gradual evolution from the full gap to the nodal gap with doping. The results will be discussed in terms of competing s- and d- channels in the general $s_\pm$ framework.