Robust Nodal Superconductivity Induced by Isovalent Doping in $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x{)}_2{\mathrm{As}}_2$ and ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$

We present the ultra-low-temperature heat-transport study of iron-based superconductors $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x{)}_2{\mathrm{As}}_2$ and ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$. For optimally doped $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$, a large residual ${\kappa }_0/T$ 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 one more nodal superconductor in iron pnictides. The similarities between isovalent Fe and P dopings strongly suggest that the nodal superconductivity in $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$ may have the same origin as in ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}{)}_2$. Furthermore, in underdoped $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$ and strongly underdoped ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$, ${\kappa }_0/T$ manifests similar nodal behavior, which result shows the robustness of nodal superconductivity in the underdoped regime and puts constraint on theoretical models.

Popular Summary

Iron-based high-temperature superconductors, the discovery of which began only in 2008, have galvanized the research on superconductivity. What microscopic mechanism(s) is responsible for the electron pairing underlying their superconductivity? Some essential clues to the answer to this question lie in the symmetry properties of the quantum-mechanical wave functions of the electron pairs. So far, the clues that are available indicate a complex picture rather than a clear origin and raise puzzles themselves. While the pair wave functions of most iron-based superconductors seem to show the highest symmetry possible–the kind called “nodeless $s\pm$-wave symmetry,” five compounds, ${\mathrm{KFe}}_2{\mathrm{As}}_2$, ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$, ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$, LaFePO, and LiFeP stand out in contrast, with their pair wave functions displaying lower symmetry that is referred to as “nodal.” In this paper, we present new experimental data on nodal superconductors that suggests some significant common threads in the diverse clues and puts relevant constraints on theoretical modeling.

The evidence of nodal superconductivity in the above five compounds raises two interesting questions specifically: First, does the presence of P (as in the last three compounds) play any special role in inducing nodal behavior? Second, since $\mathrm{BaF}{\mathrm{e}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ is derived from substitutional isovalent doping of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ by P, how does the symmetry evolve as the doping is varied? With these questions in mind, we have substituted Fe with Ru in the ${\mathrm{Fe}}_2{\mathrm{As}}_2$ layers as an alternative way to isovalent doping of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ by substituting As with P, and chosen for our investigation two Ru-doped compounds: the optimally doped $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$, and an underdoped $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$. For comparison, we have also investigated a P-doped ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$, which is more underdoped than $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$.

The measurements we have performed are thermal-conductivity measurements at ultra-low temperatures down to 50 mK and for a range of magnetic-field strength. The data demonstrates, for all three compounds, an unambiguous linear dependence of the thermal conductivity on temperature when it approaches absolute zero–a strong evidence for the nodal behavior in the pair wave functions of these compounds. The existence of nodal superconductivity in the optimally doped $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$ suggests a common origin with the nodal superconductivity induced by P doping, rather than a special element-specific role of P. And, clearly, nodal superconductivity persists robustly as the doping is decreased, from that in $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$, to that in the underdoped $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$, and to that in the strongly underdoped ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$. This robustness goes against a recent empirical proposal for how a transition from nodeless to nodal superconductivity may be induced by tuning the relative height of the pnictogen layers to the iron layers.

Figure 1

Isovalent doping in the ${\mathrm{Fe}}_2{\mathrm{As}}_2$ slabs of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, by substituting As with P, or Fe with Ru. Both ways can induce superconductivity, and both result in similar phase diagrams.

Figure 2

In-plane electronic resistivity of $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$, $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$, and ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$ single crystals. The low-temperature superconducting transitions are shown in the inset. Defined by $\rho =0$, the transition temperatures $T_c=20$, 17, and 4 K are obtained; correspondingly, these three samples are named OP20K, UD17K, and UD4K, respectively. The solid line is a fit of the data between 30 and 90 K to $\rho (T)={\rho }_0+A{T}^n$ for the OP20K sample.

Figure 3

Low-temperature in-plane thermal conductivity of (a) $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$ (called sample OP20K in the paper), (b) $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$ (sample UD17K), and (c) ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$ (sample UD4K) in zero and finite magnetic fields applied along the $c$ axis. The solid lines are $\kappa /T=a+bT$ fit to all the curves, respectively. The dashed horizontal lines are the normal-state Wiedemann-Franz law expectation $L_0/{\rho }_0$, where $L_0$ is the Lorenz number, $2.45\times {10}^{-8}\mathrm{W}\Omega {\mathrm{K}}^{-2}$, and normal-state ${\rho }_0=44$, 115, and $74\mu \Omega \mathrm{cm}$, respectively.

Figure 4

Normalized residual ${\kappa }_0/T$ of $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$ (called sample OP20K in the paper), $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$ (sample UD17K), and ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$ (sample UD4K) as a function of $H/H_{c2}$. Similar data of an overdoped $d$-wave cuprate superconductor Tl-2201 [33], and ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}{)}_2$ [16] are also shown for comparison. The behaviors of ${\kappa }_0(H)/T$ in OP20K, UD17K, and UD4K clearly mimic the behaviors in Tl-2201 and ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}{)}_2$. Inset: the same data points for OP20K, UD17K, UD4K, and Tl-2201 are plotted against $(H/H_{c2}{)}^{1/2}$. The lines represent the $H^{1/2}$ dependence.