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The mechanism of unconventional superconductivity in iron-basedsuperconductors (IBSs) is one of the most intriguing questions in currentmaterials research. Among non-oxide IBSs, (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ hasbeen intensively studied because of its high superconducting transitiontemperature and fascinating evolution of the superconducting gap structure frombeing fully isotropic at optimal doping ($x\approx$0.4) to becoming nodal at$x > $0.8. Although this marked evolution was identified in several independentexperiments, there are no details of the gap evolution to date because of thelack of high-quality single crystals covering the entire K-doping range of thesuperconducting dome. We conducted a systematic study of the London penetrationdepth, $\lambda (T)$, across the full phase diagram for differentconcentrations of point-like defects introduced by 2.5 MeV electronirradiation. Fitting the low-temperature variation with the power law, $\Delta\lambda \sim T^{n}$, we find that the exponent $n$ is the highest and $T_c$suppression rate with disorder is the smallest at optimal doping, and theyevolve with doping being away from optimal, which is consistent with increasinggap anisotropy, including an abrupt change around $x\simeq 0.8$, indicating theonset of nodal behavior. Our analysis using a self-consistent $t$-matrixapproach suggests the ubiquitous and robust nature of s$_{\pm}$ pairing in IBSsand argues against a previously suggested transition to a $d-$wave state near$x=1$ in this system.

Energy Gap Evolution Across the Superconductivity Dome in Single Crystals of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$