Robust nodal superconductivity induced by isovalent doping in Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ and BaFe$_2$(As$_{1-x}$P$_x$)$_2$

We present the ultra-low-temperature heat transport study of iron-based superconductors Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ and BaFe$_2$(As$_{1-x}$P$_x$)$_2$. For optimally doped Ba(Fe$_{0.64}$Ru$_{0.36}$)$_2$As$_2$, a large residual linear term $\kappa_0/T$ at zero field and a $\sqrt{H}$ dependence of $\kappa_0(H)/T$ are observed, which provide strong evidences for nodes in the superconducting gap. This result demonstrates that the isovalent Ru doping can also induce nodal superconductivity, as P does in BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$. Furthermore, in underdoped Ba(Fe$_{0.77}$Ru$_{0.23}$)$_2$As$_2$ and heavily underdoped BaFe$_2$(As$_{0.82}$P$_{0.18}$)$_2$, $\kappa_0/T$ manifests similar nodal behavior, which shows the robustness of nodal superconductivity in the underdoped regime and puts constraint on theoretical models.