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
X. Qiu, S. Y. Zhou, H. Zhang, B. Y. Pan, X. C. Hong, Y. F. Dai, Man Jin Eom, Jun Sung Kim, Z. R. Ye, Y. Zhang, D. L. Feng, S. Y. Li
aa r X i v : . [ c ond - m a t . s up r- c on ] D ec Robust nodal superconductivity induced by isovalent doping inBa(Fe − x Ru x ) As and BaFe (As − x P x ) X. Qiu, S. Y. Zhou, H. Zhang, B. Y. Pan, X. C. Hong, Y. F. Dai, Man Jin Eom, Jun Sung Kim, Z. R. Ye, Y. Zhang, D. L. Feng, S. Y. Li , ∗ Department of Physics, State Key Laboratory of Surface Physics,and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, China Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea (Dated: June 20, 2018)We present the ultra-low-temperature heat transport study of iron-based superconductorsBa(Fe − x Ru x ) As and BaFe (As − x P x ) . For optimally doped Ba(Fe . Ru . ) As , a large resid-ual linear term κ /T at zero field and a √ H dependence of κ ( H ) /T are observed, which providestrong evidences for nodes in the superconducting gap. This result demonstrates that the isovalentRu doping can also induce nodal superconductivity, as P does in BaFe (As . P . ) . Furthermore,in underdoped Ba(Fe . Ru . ) As and heavily underdoped BaFe (As . P . ) , κ /T manifestssimilar nodal behavior, which shows the robustness of nodal superconductivity in the underdopedregime and puts constraint on theoretical models. PACS numbers: 74.70.Xa, 74.25.fc, 74.20.Rp
Since the discovery of high- T c superconductivity iniron pnictides [1, 2], the electronic pairing mechanismhas been a central issue [3]. One key to understand itis to clarify the symmetry and structure of the super-conducting gap [4]. However, even for the most studied(Ba,Sr,Ca,Eu)Fe As (122) system, the situation is stillfairly complex [4].Near optimal doping, for both hole- and electron-doped122 compounds, the angle-resolved photon emission spec-troscopy (ARPES) experiments clearly demonstratedmultiple nodeless superconducting gaps [5, 6], which wasfurther supported by bulk measurements such as ther-mal conductivity [7–9]. On the overdoped side, nodal su-perconductivity was found in the extremely hole-dopedKFe As [10, 11], while strongly anisotropic gap [9],or isotropic gaps with significantly different magnitudes[12, 13] were suggested in the heavily electron-dopedBa(Fe − x Co x ) As . On the underdoped side, recent heattransport measurements claimed possible nodes in the su-perconducting gap of hole-doped Ba − x K x Fe As with x < − x Co x ) As [9].Intriguingly, nodal superconductivity was also foundin optimally doped BaFe (As . P . ) ( T c = 30 K)[15, 16], in which the superconductivity is induced byisovalent P doping. The ARPES experiments have givenconflicting results on the position of the nodes [17, 18].Moreover, previously LaFePO ( T c ∼ T c ∼ FIG. 1: (Color online). Isovalent doping in the Fe As slabsof BaFe As , by substituting As with P, or Fe with Ru. Bothways can induce superconductivity, and result in similar phasediagrams. pnictide superconductors, except for KFe As , is inducedwhen the pnictogen height h P n from the iron plane de-creases below a threshold value of ∼ h P n , for exam-ple, in underdoped BaFe (As − x P x ) . Therefore, it isimportant to investigate the doping evolution of the su-perconducting gap structure in BaFe (As − x P x ) . In an-other aspect, since isovalent substituting Fe with Ru inBaFe As , as shown in Fig. 1, can also decrease h P n andresult in similar phase diagram [27–29], it will be very in-teresting to check whether the gap of Ba(Fe − x Ru x ) As has nodes.In this Letter, we report the demon-stration of nodal superconductivity in opti-mally doped Ba(Fe . Ru . ) As , underdopedBa(Fe . Ru . ) As , and heavily underdopedBaFe (As . P . ) by thermal conductivity mea-surements down to 50 mK. Our finding of nodal gap in BaFe (As P ) UD4K Ba(Fe Ru ) As UD17K Ba(Fe Ru ) As OP20K r ( mW c m ) T (K)
FIG. 2: (Color online). In-plane resistivity ofBa(Fe . Ru . ) As , Ba(Fe . Ru . ) As , andBaFe (As . P . ) single crystals. The low-temperaturesuperconducting transitions are shown in the inset. Definedby ρ = 0, the transition temperatures T c = 20, 17, and 4K are obtained, therefore these three samples are named asOP20K, UD17K, and UD4K, respectively. The solid line is afit of the data between 30 and 90 K to ρ ( T ) = ρ + AT n forthe OP20K sample. Ba(Fe . Ru . ) As suggests a common origin of thenodal superconductivity induced by isovalent P and Rudoping. The nodal gap in Ba(Fe . Ru . ) As andBaFe (As . P . ) shows no transition from nodal tonodeless state in the underdoped regime.Single crystals of Ba(Fe − x Ru x ) As andBaFe (As − x P x ) were grown according to the methodsdescribed in Refs. [30, 31]. The Ru and P dopinglevels were determined by energy dispersive X-rayspectroscopy. The sample was cleaved to a rectangularshape with typical dimensions ∼ × in the ab -plane, and 40 to 80 µ m in c -axis. In-plane thermalconductivity was measured in a dilution refrigerator,using a standard four-wire steady-state method withtwo RuO chip thermometers, calibrated in situ againsta reference RuO thermometer. Magnetic fields wereapplied along the c -axis. To ensure a homogeneous fielddistribution in the samples, all fields were applied attemperature above T c .Fig. 2 shows the in-plane resistivity ρ ( T )of Ba(Fe . Ru . ) As , Ba(Fe . Ru . ) As , andBaFe (As . P . ) single crystals. The transition tem-peratures defined by ρ = 0 are T c = 20, 17, and 4K, therefore we name these three samples as OP20K,UD17K, and UD4K, respectively. One can see clearresistivity anomalies in UD4K and UD17K, but notin OP20K, which manifest the gradual suppression ofspin-density-wave (SDW) order upon P or Ru doping[28, 29, 32]. For OP20K, the resistivity data between30 and 90 K are fitted to ρ ( T ) = ρ + AT n , which gives a Ru ) As L / r
12 T 9 T 6 T 4 T 2 T 1 T 0 T (b) Ba(Fe Ru ) As L / r
12 T 7 T 4 T 2 T 1 T 0 T k / T ( m W / K c m ) (c) BaFe (As P ) L / r T (K)
FIG. 3: (Color online). Low-temperature in-plane thermalconductivity of Ba(Fe . Ru . ) As , Ba(Fe . Ru . ) As ,and BaFe (As . P . ) in zero and magnetic fields appliedalong the c -axis. The solid lines are κ/T = a + bT fit to allthe curves, respectively. The dash lines are the normal-stateWiedemann-Franz law expectation L / ρ , with L the Lorenznumber 2.45 × − WΩK − and normal-state ρ = 44, 115,and 74 µ Ωcm, respectively. residual resistivity ρ = 43.7 ± µ Ωcm and n = 1.31 ± ρ ( T ) is similar to that observed in BaFe (As − x P x ) nearoptimal doping, which may reflect the presence of anti-ferromagnetic spin fluctuations near a quantum criticalpoint [32].The resistivity of these samples were also measured inmagnetic fields, the highest up to 14.5 T, in order todetermine their upper critical field H c and normal-state ρ . For OP20K, UD17K, and UD4K, we estimate H c =23, 19, and 5 T, and normal-state ρ = 44, 115, and 74 µ Ωcm, respectively.Fig. 3 shows the temperature dependence of the in-plane thermal conductivity for OP20K, UD17K, andUD4K in zero and magnetic fields, plotted as κ/T vs T . All the curves are roughly linear, as previously ob-served in BaFe . Ni . As [8], KFe As [10], and over-doped Ba(Fe − x Co x ) As single crystals [9, 12]. There-fore we fit all the curves to κ/T = a + bT α − with α fixedto 2. The two terms aT and bT α represent contributionsfrom electrons and phonons, respectively. Here we onlyfocus on the electronic term.For OP20K in zero field, the fitting gives a residuallinear term κ /T = 0.266 ± − cm − . Thisvalue is more than 40% of the normal-state Wiedemann-Franz law expectation κ N /T = L / ρ = 0.56 mWK − cm − , with L the Lorenz number 2.45 × − WΩK − and normal-state ρ = 44 µ Ωcm. For optimallydoped BaFe (As . P . ) single crystal, similar valueof κ /T ≈ − cm − was obtained, which isabout 30% of its normal-state κ N /T [16]. The signif-icant κ /T of Ba(Fe . Ru . ) As in zero field is at-tributed to nodal quasiparticles, which is a strong evi-dence for nodes in the superconducting gap [33].With decreasing doping level, for UD17K and UD4K, κ /T = 35 ± ± µ W K − cm − are obtained,as seen in Figs. 3(b) and 3(c). These values are about17% and 22% of their normal-state κ N /T , respectively.We note Hashimoto et al. already mentioned that thesuperconducting gap in overdoped SrFe (As . P . ) andBaFe (As . P . ) has nodes [22]. Therefore, our obser-vation of significant κ /T in the underdoped regime, par-ticularly in the heavily underdoped BaFe (As . P . ) ,further shows the robustness of nodal superconductivityagainst doping in P- and Ru-doped 122 iron pnictides.The field dependence of κ /T can provide further sup-port for the gap nodes [33]. In Fig. 4, the normalized( κ /T ) / ( κ N /T ) of OP20K, UD17K, and UD4K are plot-ted as a function of H/H c . For UD4K, κ/T saturatesabove H = 3 T, as seen in Fig. 3(c), which is determinedas its bulk H c . For OP20K and UD17K, we use their H c estimated from resistivity measurements. To choosea slightly different bulk H c does not affect our discussionon the field dependence of κ /T . Similar data of an over-doped d -wave cuprate superconductor Tl-2201 [34], andBaFe (As . P . ) [16] are also plotted for comparison.For a nodal superconductor such as Tl-2201 in mag-netic field, delocalized states exist out the vortex coresand 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 vor-tices will yield an H / growth in quasiparticle density ofstates (the Volovik effect [35]), thus the H / field depen-dence of κ /T . From Fig. 4, the behavior of κ ( H ) /T inOP20K, UD17K, and UD4K clearly mimics that in Tl-2201 and BaFe (As . P . ) . In the inset of Fig. 4, the κ ( H ) /T of OP20K, UD17K, and UD4K obey the H / dependence at low field, which supports the existence ofgap nodes.To our knowledge, so far there are five iron-basedsuperconductors displaying nodal superconductivity, in-cluding KFe As [10, 11], underdoped Ba − x K x Fe As ( x < (As − x P x ) [15, 16], LaFePO [19– Tl2201 BaFe (As P ) Ba(Fe Ru ) As BaFe (As P ) Ba(Fe Ru ) As ( k / T ) / ( k N / T ) H/H c2 ( k / T ) / ( k N / T ) (H/H c2 ) FIG. 4: (Color online). Normalized residual linear term κ /T of Ba(Fe . Ru . ) As , Ba(Fe . Ru . ) As , andBaFe (As . P . ) as a function of H/H c . Similar dataof an overdoped d -wave cuprate superconductor Tl-2201 [34],and BaFe (As . P . ) [16] are also shown for comparison.The behaviors of κ ( H ) /T in OP20K, UD17K, and UD4Kclearly mimic that in Tl-2201 and BaFe (As . P . ) . In-set: the same data of OP20K, UD17K, UD4K, and Tl-2201plotted against ( H/H c ) / . The lines represent the H / de-pendence. c -axis nodes” in underdopedand overdoped Ba(Fe − x Co x ) As as suggested by c -axisheat transport experiments [36]. For the extremely hole-doped KFe As , the nodal gap may have d -wave symme-try, and result from the direct intra-pocket interaction viaantiferromagnetic fluctuations, due to the lack of electronpockets [10, 37, 38]. For underdoped Ba − x K x Fe As ,it is still not clear how the superconducting gap trans-forms from nodeless to nodal at x ≈ .
16 [14]. Therest three compounds, BaFe (As − x P x ) , LaFePO, andLiFeP, have stimulated various interpretations of the ef-fect of isovalent P doping [23–26], and may represent apeculiar superconducting mechanism.Our new finding of nodal superconductivity inBa(Fe − x Ru x ) As reveals the similarity between the iso-valently Ru- and P-doped iron pnictides. In this sense,the P doping is not that special for inducing nodal su-perconductivity now, and the puzzle of P doping in iron-based superconductors has been partially unwrapped.What next one needs to do is to find out the common ori-gin for the nodal superconductivity in these isovalentlydoped iron pnictides.Due to the smaller size of P ion than As ion, one com-mon structural feature of the P-doped compounds is thedecrease of pnictogen height h P n and increase of As-Fe-As angle [32, 39, 40]. The substitution of larger Ru ionfor Fe ion in Ba(Fe − x Ru x ) As results in the increaseof a lattice parameter and decrease of c lattice param-eter, thus the decrease of pnictogen height and increaseof As-Fe-As angle [28]. Therefore, both the P and Rudopants cause the same trend of structure change in ironarsenides.With such structure change, the Fermi surface (FS)evolution upon isovlant P and Ru doping is rather del-icate. The main feature, hole pockets around Bril-louin zone (BZ) center and electron pockets aroundBZ corners, remains in LaFePO [41], BaFe (As − x P x ) [17, 18, 31], Ba(Fe − x Ru x ) As [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 pnictogenheight [23]. For BaFe (As − x P x ) , Suzuki et al. haveproposed three-dimensional nodal structure in the largelywarped hole Fermi surface and no nodes on the electronFermi surface [26]. This is supported by recent ARPESexperiments, which found nodal gap in the expanded α hole pocket at k z = π in BaFe (As . P . ) [18], how-ever, it conflicts with earlier ARPES results which haveconstrained the nodes on the electron pockets [17]. SinceARPES experiments did not find significant changes inthe shape of the Fermi surface or in the Fermi velocityover a wide range of doping levels in Ba(Fe − x Ru x ) As ,Dhaka et al. speculated that its superconducting mecha-nism relies on magnetic dilution which leads to the reduc-tion of the effective Stoner enhancement [43]. In LiFeP,the middle hole pocket has significantly lower mass en-hancement than the other pockets, which implies thatthe electron-hole scatter rate is suppress for this pocketand may result in the lower T c and nodal gap [44].While the clues for nodal superconductivity are notvery clear from the FS topology except for KFe As ,Hashimoto et al. gathered the available data for the low-energy quasiparticle excitations in several iron-pnictidesuperconductors, and suggested that there is a thresh-old value of h P n ∼ h P n in underdopedBa(Fe − x Ru x ) As and BaFe (As − x P x ) . To test thisidea, we estimate h P n = 1.317, 1.333, 1.340 ˚A 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 areslightly larger than the proposed threshold value 1.33˚A. In particular, the h P n of UD4K is comparable tothat of overdoped Ba(Fe . Co . ) As , which is a node-less superconductor [22]. Since our thermal conductivitydata suggest UD17K and UD4K are nodal superconduc-tors, h P n should not be considered as the only parame-ter for tuning between nodeless and nodal superconduct-ing states. By saying this, we do not deny its impor-tance, since h P n of the underdoped Ba(Fe − x Ru x ) As and BaFe (As − x P x ) are still very close to the thresholdvalue 1.33 ˚A. More careful considerations of the struc- tural parameters, FS topology, and local interactions areneeded to clarify the origin of the nodal superconductiv-ity in isovalently doped iron pnictides.In summary, we have measured the thermal conductiv-ity of Ba(Fe . Ru . ) As , Ba(Fe . Ru . ) As , andBaFe (As . P . ) single crystals down to 50 mK. A sig-nificant κ /T at zero field and an H / field dependenceof κ ( H ) /T at low field give strong evidences for nodalsuperconductivity in all three compounds. Comparingwith previous P-doped iron pnictides, our new findingsuggest that the nodal superconductivity induced by iso-valent Ru and P doping may have the same origin. Withdecreasing doping level, nodal superconducting state per-sists robustly in heavily underdoped BaFe (As . P . ) ,suggesting that the h P n is not the only tuning parame-ter, thus putting constraint on theoretical models. Find-ing out the origin of these nodal superconducting stateswill be crucial for getting a complete electronic pairingmechanism in the iron-based high- T c superconductors.This work is supported by the Natural ScienceFoundation of China, the Ministry of Science andTechnology of China (National Basic Research ProgramNo: 2009CB929203 and 2012CB821402), Program forProfessor of Special Appointment (Eastern Scholar)at Shanghai Institutions of Higher Learning, andSTCSM of China. 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