Evidence of competing interactions within hole Fermi-surface sheets in the vicinity of KFe$_2$As$_2$

We have investigated the superconducting(SC)-gap anisotropy of Ba$_{0.07}$K$_{0.93}$Fe$_2$As$_2$, Ba$_{0.12}$K$_{0.88}$Fe$_2$As$_2$, and Ba$_{0.24}$K$_{0.76}$Fe$_2$As$_2$ using laser-based angle-resolved photoemission spectroscopy. Whereas in the end material K122, the inner and middle Fermi surfaces (FSs) have substantially anisotropic SC gaps, the outer FS has an almost zero gap, and the middle FS has octet-line nodes, in the 7% Ba-doped sample, the SC gap of the inner FS becomes almost isotropic, the middle has a still anisotropic gap and nodes, and the outer has a finite gap and nodes. In addition, in the 12% and 24% Ba-doped samples, the SC gap of the middle FS becomes almost isotropic. We attribute this doping dependence to the existence of competing pairing interactions in this doping region.