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.

Since the discovery of high-T c superconductivity in iron pnictides [1,2], the electronic pairing mechanism has been a central issue [3].One key to understand it is to clarify the symmetry and structure of the superconducting gap [4].However, even for the most studied (Ba,Sr,Ca,Eu)Fe 2 As 2 (122) system, the situation is still fairly complex [4].
Intriguingly, nodal superconductivity was also found in optimally doped BaFe 2 (As 0.67 P 0.33 ) 2 (T c = 30 K) [15,16], in which the superconductivity is induced by isovalent P doping.The ARPES experiments have given conflicting results on the position of the nodes [17,18].Moreover, previously LaFePO (T c ∼ 6 K) displays clear nodal behavior [19][20][21], and recently there is penetration depth evidence for nodes in the superconducting gap of LiFeP (T c ∼ 4.5 K) [22].The nodal superconductivity in these P-doped compounds are very striking, which raises the puzzling question why the P doping is so special in iron-based superconductors.The theoretical explanations of this puzzle are far from consensus [23][24][25][26].
A recent proposal is that the nodal state in iron- pnictide superconductors, except for KFe 2 As 2 , is induced when the pnictogen height h P n from the iron plane decreases below a threshold value of ∼ 1.33 Å [22].According to this proposal, there may exist a transition from nodal to nodeless state tuned by h P n , for example, in underdoped BaFe 2 (As 1−x P x ) 2 .Therefore, it is important to investigate the doping evolution of the superconducting gap structure in BaFe 2 (As 1−x P x ) 2 .In another aspect, since isovalent substituting Fe with Ru in BaFe 2 As 2 , as shown in Fig. 1, can also decrease h P n and result in similar phase diagram [27][28][29], it will be very interesting to check whether the gap of Ba(Fe and BaFe 2 (As 1−x P x ) 2 were grown according to the methods described in Refs.[30,31].The Ru and P doping levels were determined by energy dispersive X-ray spectroscopy.The sample was cleaved to a rectangular shape with typical dimensions ∼ 1.50 × 0.7 mm 2 in the ab-plane, and 40 to 80 µm in c-axis.In-plane thermal conductivity was measured in a dilution refrigerator, using a standard four-wire steady-state method with two RuO 2 chip thermometers, calibrated in situ against a reference RuO 2 thermometer.Magnetic fields were applied along the c-axis.To ensure a homogeneous field distribution in the samples, all fields were applied at temperature above T c .Fig. 2 shows the in-plane resistivity ρ(T ) of Ba(Fe 0.64 Ru 0.36 ) 2 As 2 , Ba(Fe 0.77 Ru 0.23 ) 2 As 2 , and BaFe 2 (As 0.82 P 0.18 ) 2 single crystals.The transition temperatures defined by ρ = 0 are T c = 20, 17, and 4 K, therefore we name these three samples as OP20K, UD17K, and UD4K, respectively.One can see clear resistivity anomalies in UD4K and UD17K, but not in OP20K, which manifest the gradual suppression of spin-density-wave (SDW) order upon P or Ru doping [28,29,32].For OP20K, the resistivity data between 30 and 90 K are fitted to ρ(T ) = ρ 0 + AT n , which gives a residual resistivity ρ 0 = 43.7 ± 0.1 µΩcm and n = 1.31 ± 0.1.Such a non-Fermi-liquid temperature dependence of ρ(T ) is similar to that observed in BaFe 2 (As 1−x P x ) 2 near optimal doping, which may reflect the presence of antiferromagnetic spin fluctuations near a quantum critical point [32].The resistivity of these samples were also measured in magnetic fields, the highest up to 14.5 T, in order to determine their upper critical field H c2 and normal-state ρ 0 .For OP20K, UD17K, and UD4K, we estimate H c2 = 23, 19, and 5 T, and normal-state ρ 0 = 44, 115, and 74 µΩcm, respectively.Fig. 3 shows the temperature dependence of the inplane thermal conductivity for OP20K, UD17K, and UD4K in zero and magnetic fields, plotted as κ/T vs T .All the curves are roughly linear, as previously observed in BaFe 1.9 Ni 0.1 As 2 [8], KFe 2 As 2 [10], and over-doped Ba(Fe 1−x Co x ) 2 As 2 single crystals [9,12].Therefore we fit all the curves to κ/T = a + bT α−1 with α fixed to 2. The two terms aT and bT α represent contributions from electrons and phonons, respectively.Here we only focus on the electronic term.
The field dependence of κ 0 /T can provide further support for the gap nodes [33].In Fig. 4, the normalized (κ 0 /T )/(κ N 0 /T ) of OP20K, UD17K, and UD4K are plotted as a function of H/H c2 .For UD4K, κ/T saturates above H = 3 T, as seen in Fig. 3(c), which is determined as its bulk H c2 .For OP20K and UD17K, we use their H c2 estimated from resistivity measurements.To choose a slightly different bulk H c2 does not affect our discussion on the field dependence of κ 0 /T .Similar data of an overdoped d-wave cuprate superconductor Tl-2201 [34], and BaFe 2 (As 0.67 P 0.33 ) 2 [16] are also plotted for comparison.
For a nodal superconductor such as Tl-2201 in magnetic field, delocalized states exist out the vortex cores and dominate the heat transport in the vortex state, in contrast to the s-wave superconductor.At low field, the Doppler shift due to superfluid flow around the vortices will yield an H 1/2 growth in quasiparticle density of states (the Volovik effect [35]), thus the H 1/2 field dependence of κ 0 /T .From Fig. 4, the behavior of κ 0 (H)/T in OP20K, UD17K, and UD4K clearly mimics that in Tl-2201 and BaFe 2 (As 0.67 P 0.33 ) 2 .In the inset of Fig. 4, the κ 0 (H)/T of OP20K, UD17K, and UD4K obey the H 1/2 dependence at low field, which supports the existence of gap nodes.
21], and LiFeP [22].Here we only consider the "in-plane nodes", not counting the "c-axis nodes" in underdoped and overdoped Ba(Fe 1−x Co x ) 2 As 2 as suggested by c-axis heat transport experiments [36].For the extremely holedoped KFe 2 As 2 , the nodal gap may have d-wave symmetry, and result from the direct intra-pocket interaction via antiferromagnetic fluctuations, due to the lack of electron pockets [10,37,38].For underdoped Ba 1−x K x Fe 2 As 2 , it is still not clear how the superconducting gap transforms from nodeless to nodal at x ≈ 0.16 [14].The rest three compounds, BaFe 2 (As 1−x P x ) 2 , LaFePO, and LiFeP, have stimulated various interpretations of the effect of isovalent P doping [23][24][25][26], and may represent a peculiar superconducting mechanism.
Our new finding of nodal superconductivity in Ba(Fe 1−x Ru x ) 2 As 2 reveals the similarity between the isovalently Ru-and P-doped iron pnictides.In this sense, the P doping is not that special for inducing nodal superconductivity now, and the puzzle of P doping in ironbased superconductors has been partially unwrapped.What next one needs to do is to find out the common origin for the nodal superconductivity in these isovalently doped iron pnictides.
Due to the smaller size of P ion than As ion, one common structural feature of the P-doped compounds is the decrease of pnictogen height h P n and increase of As-Fe-As angle [32,39,40].The substitution of larger Ru ion for Fe ion in Ba(Fe 1−x Ru x ) 2 As 2 results in the increase of a lattice parameter and decrease of c lattice param-eter, thus the decrease of pnictogen height and increase of As-Fe-As angle [28].Therefore, both the P and Ru dopants cause the same trend of structure change in iron arsenides.
With such structure change, the Fermi surface (FS) evolution upon isovlant P and Ru doping is rather delicate.The main feature, hole pockets around Brillouin zone (BZ) center and electron pockets around BZ corners, remains in LaFePO [41], BaFe 2 (As 1−x P x ) 2 [17,18,31], Ba(Fe 1−x Ru x ) 2 As 2 [42,43], and LiFeP [44].For LaFePO, Kuroki et al. have attributed the low-T c nodal pairing to the lack of Fermi surface γ around (π, π) in the unfolded Brillouin zone, due to the low pnictogen height [23].For BaFe 2 (As 1−x P x ) 2 , Suzuki et al. have proposed three-dimensional nodal structure in the largely warped hole Fermi surface and no nodes on the electron Fermi surface [26].This is supported by recent ARPES experiments, which found nodal gap in the expanded α hole pocket at k z = π in BaFe 2 (As 0.7 P 0.3 ) 2 [18], however, it conflicts with earlier ARPES results which have constrained the nodes on the electron pockets [17].Since ARPES experiments did not find significant changes in the shape of the Fermi surface or in the Fermi velocity over a wide range of doping levels in Ba(Fe 1−x Ru x ) 2 As 2 , Dhaka et al. speculated that its superconducting mechanism relies on magnetic dilution which leads to the reduction of the effective Stoner enhancement [43].In LiFeP, the middle hole pocket has significantly lower mass enhancement than the other pockets, which implies that the electron-hole scatter rate is suppress for this pocket and may result in the lower T c and nodal gap [44].
While the clues for nodal superconductivity are not very clear from the FS topology except for KFe 2 As 2 , Hashimoto et al. gathered the available data for the lowenergy quasiparticle excitations in several iron-pnictide superconductors, and suggested that there is a threshold value of h P n ∼ 1.33 Å, below which all the superconductors exhibit nodal superconducting state [22].If this is the case, there may exist a transition from nodal to nodeless state tuned by h P n in underdoped Ba(Fe 1−x Ru x ) 2 As 2 and BaFe 2 (As 1−x P x ) 2 .To test this idea, we estimate h P n = 1.317, 1.333, 1.340 Å for OP20K, UD17K, UD4K from the roughly linear increase of h P n with decreasing Ru or P doping [28,32].
One can see that both h P n of UD17K and UD4K are slightly larger than the proposed threshold value 1.33 Å.In particular, the h P n of UD4K is comparable to that of overdoped Ba(Fe 0.89 Co 0.11 ) 2 As 2 , which is a nodeless superconductor [22].Since our thermal conductivity data suggest UD17K and UD4K are nodal superconductors, h P n should not be considered as the only parameter for tuning between nodeless and nodal superconducting states.By saying this, we do not deny its importance, since h P n of the underdoped Ba(Fe 1−x Ru x ) 2 As 2 and BaFe 2 (As 1−x P x ) 2 are still very close to the threshold value 1.33 Å.More careful considerations of the struc-tural parameters, FS topology, and local interactions are needed to clarify the origin of the nodal superconductivity in isovalently doped iron pnictides.
In summary, we have measured the thermal conductivity of Ba(Fe 0.64 Ru 0.36 ) 2 As 2 , Ba(Fe 0.77 Ru 0.23 ) 2 As 2 , and BaFe 2 (As 0.82 P 0.18 ) 2 single crystals down to 50 mK.A significant κ 0 /T at zero field and an H 1/2 field dependence of κ 0 (H)/T at low field give strong evidences for nodal superconductivity in all three compounds.Comparing with previous P-doped iron pnictides, our new finding suggest that the nodal superconductivity induced by isovalent Ru and P doping may have the same origin.With decreasing doping level, nodal superconducting state persists robustly in heavily underdoped BaFe 2 (As 0.82 P 0.18 ) 2 , suggesting that the h P n is not the only tuning parameter, thus putting constraint on theoretical models.Finding out the origin of these nodal superconducting states will be crucial for getting a complete electronic pairing mechanism in the iron-based high-T c superconductors. This

FIG. 1 :
FIG. 1: (Color online).Isovalent doping in the Fe2As2 slabs of BaFe2As2, by substituting As with P, or Fe with Ru.Both ways can induce superconductivity, and result in similar phase diagrams.
1−x Ru x ) 2 As 2 Fe 0.64 Ru 0.36 ) 2 As 2 , underdoped Ba(Fe 0.77 Ru 0.23 ) 2 As 2 , and heavily underdoped BaFe 2 (As 0.82 P 0.18 ) 2 by thermal conductivity measurements down to 50 mK.Our finding of nodal gap in Ba(Fe 0.64 Ru 0.36 ) 2 As 2 suggests a common origin of the nodal superconductivity induced by isovalent P and Ru doping.The nodal gap in Ba(Fe 0.77 Ru 0.23 ) 2 As 2 and BaFe 2 (As 0.82 P 0.18 ) 2 shows no transition from nodal to nodeless state in the underdoped regime.Ru x ) 2 As 2 , LaFePO [19-As 0.67 P 0.33 ) 2 Ba(Fe 0.64 Ru 0.36 ) 2 As 2 BaFe 2 (As 0.82 P 0.18 ) 2 Ba(Fe 0.77 Ru 0.23 ) 2 As 2 work is supported by the Natural Science Foundation of China, the Ministry of Science and Technology of China (National Basic Research Program No: 2009CB929203 and 2012CB821402), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and STCSM of China.The work at Postech was supported by Leading Foreign Research Institute Recruitment Program(2010-00471), Basic Science Research Programs (2010-0005669) through the National Research Foundation of Korea(NRF)