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Doping evolution of the superconducting gap structure in heavily hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$: heat transport study

We performed systematic thermal conductivity measurements on heavily hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals with 0.747 $\leq x \leq$ 0.974. At $x$ = 0.747, the $κ_0/T$ is negligible, indicating nodeless superconducting gap. A small residual linear term $κ_0/T$ ($\approx$ 0.035 mW/K$^2$ cm) appears at $x$ = 0.826, and it increases slowly up to $x$ = 0.974, followed by a drastic increase of more than 20 times to the pure KFe$_2$As$_2$ ($x$ = 1.0). This doping dependence of $κ_0/T$ clearly shows that the nodal gap appears near $x = 0.8$, likely associated with the change of Fermi surface topology. The small values of $κ_0/T$ from $x$ = 0.826 to 0.974 support a "$\curlyvee$"-shaped nodal $s$-wave gap recently revealed by angle-resolved photoemission spectroscopy experiments at $x$ = 0.9. Furthermore, the drastic increase of $κ_0/T$ from $x$ = 0.974 to 1.0 is inconsistent with a symmetry-imposed $d$-wave gap in KFe$_2$As$_2$, and the possible nodal gap structure in KFe$_2$As$_2$ is discussed.