Superconductivity in Ta3Pd3Te14 with quasi-one-dimensional PdTe2 chains

We report bulk superconductivity at 1.0 K in a low-dimensional ternary telluride Ta3Pd3Te14 containing edge-sharing PdTe2 chains along crystallographic b axis, similar to the recently discovered superconductor Ta4Pd3Te16. The electronic heat capacity data show an obvious anomaly at the transition temperature, which indicates bulk superconductivity. The specific-heat jump is ΔC/(γnTc) ≈ 1.35, suggesting a weak coupling scenario. By measuring the low-temperature thermal conductivity, we conclude that Ta3Pd3Te14 is very likely a dirty s-wave superconductor. The emergence of superconductivity in Ta3Pd3Te14 with a lower Tc, compared to that of Ta4Pd3Te16, may be attributed to the lower density of states.

In this paper, we report the observation of SC with T c = 1.0 K in layered ternary telluride Ta 3 Pd 3 Te 14 with Q1D PdTe 2 chains. The bulk SC was identified by the electronic heat capacity data, which shows an obvious anomaly at the transition temperature. The specific-heat jump Δ C/(γ n T c ) ≈ 1.35 indicates Ta 3 Pd 3 Te 14 may be a weakly coupled superconductor. In addition, the result of low-temperature thermal conductivity measurements of Ta 3 Pd 3 Te 14 crystal down to 80 mK suggests a dirty s-wave superconducting gap. We summarize our results by discussing the similarities and differences between the closely related superconductors of Ta 3 Pd 3 Te 14 and Ta 4 Pd 3 Te 16 , and compiled an extended list of their physical properties.

Results
Single crystals of Ta 3 Pd 3 Te 14 were grown using a self-flux method, rather than the vapor transport method previously used 21 . Shiny flattened needle-like crystals with a typical size of 2 × 0.15 × 0.1 mm 3 were harvested, as shown in Fig. 1(a). The X-ray diffraction (XRD) pattern at 298 K by a conventional θ-2θ scan for the crystals lying on a sample holder is shown in Fig. 1(b), in which we can observe only multiple peaks arising from the diffraction from (1 0 1) planes, consistent with the layered crystal structure of Ta 3 Pd 3 Te 14 . Ta 3 Pd 3 Te 14 crystalizes in space group P2 1 /m with a monoclinic unit cell of a = 14.088 (19) Å, b = 3.737(3) Å, c = 20.560 (19) Å, and β = 103.73(5)° at 123 K 21 . As seen in Fig. 1(d), the layered slabs compose of successively six different chains of three different types. The three types of chains are Ta-based bicapped trigonal prismatic chains, Pd-based octahedral chains, and Ta-based octahedral chains, respectively. The arrangement of the chains, in such a way that every Pd-based chain has two adjacent Ta-based chains and vice versa, constitute the layered slab as clearly depicted in Fig. 1(e). For simplicity, hereafter we define the a * axis as to be parallel to the[1 0 1] direction and the c * axis as to be perpendicular to the (1 0 1) plane. The interplane spacing at room temperature is determined to be 6.418 Å, and this value is well consistent with the calculated one of 6.397 Å using the above mentioned parameters at 123 K, when taking into account the temperature difference. To compare the obvious difference of the interlayer spacing of Ta 3 Pd 3 Te 14  and Ta 4 Pd 3 Te 16 , we plot the third reflection together, namely (− 606) and (− 309) peaks, in the inset of Fig. 1(b), from which one can easily find the interplane spacing of Ta 3 Pd 3 Te 14 is ~2% smaller than that of Ta 4 Pd 3 Te 16 , and full width at half-maximum is only 0.05°, indicating the high quality of the crystals. The chemical composition determined by an energy-dispersive X-ray spectroscopy (EDS), are collected in a number of crystals, and the average results confirm that composition of the crystals is the stoichiometric Ta 3 Pd 3 Te 14 within the measurement errors. The SEM image, shown in the upper right corner of Fig. 1(c), has a morphology with stripes along the b axis (chain direction), consistent with the preferential crystal growth along the chain direction. Figure 2(a) shows temperature dependence of electronic resistivity along the b axis (ρ b ) for the Ta 3 Pd 3 Te 14 crystal (Sample 1). The larger room temperature resistivity (1.18 μΩ m), than that (0.61 μΩ m) of Ta 4 Pd 3 Te 16 6 , indicates Ta 3 Pd 3 Te 14 is less conductive, consistent with the previous reports 21,22 . The temperature dependence of resistivity shows a metallic behavior without any obvious anomaly down to T c = 1.0 K, at which a sharp superconducting transition appears, as clearly depicted in Fig. 2(c). The value of T c is 3.6 K less than that of Ta 4 Pd 3 Te 16 . The onset, midpoint, and zero-resistance temperatures are 1.02 K, 0.94 K, and 0.81 K, respectively, and the superconducting transition width Δ T c is 0.13 K. The ρ b (T) data between 2 and 25 K can be well fitted by to ρ b = ρ 0 + AT n , giving a residual resistivity ρ 0 = 5.13 μΩ cm and n = 2.83 [ Fig. 2(b)]. The value of n more than 2 was also observed in Ta 4 Pd 3 Te 16 , which was attributed to the phonon-assisted s-d interband scattering 18 . The residual resistivity ratio (RRR) is estimated to be RRR = ρ b (300 K)/ρ 0 ~ 23, similar to that of Ta 4 Pd 3 Te 16 (see Table 1). Figure 2(d) plots the low-temperature resistivity of Ta 3 Pd 3 Te 14 crystal (Sample 1) for H || c * up to 0.1 T. Upon increasing the field, the superconducting transition is suppressed to lower temperature. The extracted upper critical fields H c2 (T) for H || c * , determined by using 90% criterion, i.e., the field at which ρ b reaches 90% of the normal state resistivity, are shown in Fig. 2(e). We applied the isotropic one-band Werthamer-Helfand-Hohenberg (WHH) formalism to roughly estimate H c2 23 . As can be seen in Fig. 2(e), H c2 for H || c * is estimated to be 0.075 T at zero temperature with the derived Maki parameter α = 1.7 and spin-orbit coupling parameter λ so = 1.2. However, by employing the orbital limiting field µ H 0 c2 orb (0)/H P BCS is calculated to be 0.077. This inconsistence between the calculated value of α and the fitted one may originate from the anisotropic effect in Ta 3 Pd 3 Te 14 . The extracted H c2 with fields applied along a * , b, and c * directions for Sample 2 are shown in Fig. 2(f), and the resistivity data of Sample 2 are not shown here. By roughly linear extrapolations, the anisotropic H c2 at zero temperature are estimated to be 0.21, 0.27 and 0.086 T for the a * , b and c * directions. Using the Ginzburg-Landau formula, the superconducting coherence length ξ are calculated to be 545, 703 and 223 Å for a * , b and c * directions, respectively, which are much larger than those of its analog Ta 4 Pd 3 Te 16 17 . The SC in Ta 3 Pd 3 Te 14 is anisotropic but as well three-dimensional in nature, similar to other superconductors with Q1D The low-temperature specific heat data of Ta 3 Pd 3 Te 14 crystals, plotted as C/T vs T, are shown in Fig. 3(a). We fit the normal-state data from 1.2 to 6.5 K, employing the usual formula C/T = γ n + βT 2 , which is represented as the red dashed line. The fitting yields an electronic heat capacity coefficient γ n = 28.2 ± 0.9 mJ mol −1 K −2 , and a phononic coefficient β = 11.14 ± 0.04 mJ mol −1 K −4 . The calculated Debye temperature Θ D = 151.6 K is close to the value of Ta 4 Pd 3 Te 16 , consistent with the fact that the structures of two tellurides are closely related. However, the value of extracted coefficient γ n is nearly 40% smaller than that of Ta 4 Pd 3 Te 16 17 . Using the relation N(E F ) = γ π /k 3 n B 2 2 for noninteracting electron systems, where k B is the Boltzmann constant, we estimated the density of states at the Fermi level N(E F ) to be about 11.9 ± 0.8 eV −1 fu −1 , which is 3.5 times that of the bare density of states N bs (E F ), obtained from the previous band-structure calculations 20 . Therefore, the larger renormalization factor [N(E F )/N bs (E F ) = 1 + λ], than that for Ta 4 Pd 3 Te 16 , suggests much stronger electron-electron correlations in Ta 3 Pd 3 Te 14 , although the recent band-structure calculations are concluded with a higher N bs (E F ) = 9.6 eV −1 fu −1 for Ta 4 Pd 3 Te 16 , thus resulting in a much lower renormalization factor 19 . To extract the electron-nonphonon coupling strength λ nph in λ, we estimate the electron-phonon coupling constant λ ph by employing the McMillan formula 26 , λ ph = [1.04 + μ * ln(Θ D /1.45T c )]/[(1 − 0.62μ * )ln(Θ D /1.45T c ) − 1.04], where the Coulombic repulsion parameter μ * is empirically set to be 0.13. The estimated value of λ ph is 0.51, a little bit smaller than that of the superconductor Ta 4 Pd 3 Te 16 6 . However, the resultant constant λ nph = λ − λ ph = 1.99 is much larger than that of Ta 4 Pd 3 Te 16 , possibly indicating much larger electron correlations in the former compound. . RRR, T c , Δ T c , H c2 , γ n , θ D , λ ph , λ nph , N bs (E F ), and Δ C/(γ n T c ) denote the residual resistivity ratio, superconducting transition temperature, transition width, upper critical field, electronic specific-heat coefficient, Debye temperature, electron-phonon coupling constant, electron-nonphonon coupling constant, density of states at Fermi level, and dimensionless specific-heat jump, respectively.

Discussion
We discuss the electronic heat capacity C el of Ta 3 Pd 3 Te 14 crystals in low-temperature range, obtained by C el = C − βT 3 . As can be seen in Fig. 3(b), a characteristic superconducting jump (Δ C el ) shows up around ~1 K, confirming the bulk SC. The Δ C el /T c is estimated to be 38.0 mJ mol −1 K −2 and the midpoint temperature of the thermodynamic transition is 1.0 K, consistent with the superconducting transition in low-temperature resistivity. The dimensionless specific-heat jump can be calculated to be 1.35, smaller than the theoretical value (1.43) of the well-known BCS theory, indicating Ta 3 Pd 3 Te 14 may be a weakly coupled superconductor. Unfortunately, due to the insufficient data points, we are unable to fit Δ C el (T) with standard gap functions to give valuable information about the gap symmetry.
To shed light on the superconducting gap structure, we measured the thermal conductivity of Ta 3 Pd 3 Te 14 single crystal (Sample 2) in zero and magnetic fields (along c * direction), the results of which are plotted as κ/T vs T in Fig. 4(a). Since all the curves presented in Fig. 4(a) are roughly linear as previously reported in Ta 4 Pd 3 Te 16   18 and some iron-based superconductors 27,28 , we fit all the curves to κ/T = a + bT α−1 by fixing α to 2. The two terms aT and bT α represent contributions from electrons and phonons, respectively 29,30 . From the curve in magnetic field H = 0.09 T, which is close to the critical field H c2 (0) for H || c * , one can see that the obtained κ 0 /T roughly meets the normal-state Wiedemann-Franz law expectation κ N0 /T = L 0 /ρ 0 = 2.44 mW K −2 cm −1 . Here, L 0 is the Lorenz number 2.45 × 10 −8 W Ω K −2 and ρ 0 = 10.04 μΩ cm is the residual resistivity of Sample 2. The verification of the Wiedemann-Franz law in the normal state demonstrates that our thermal conductivity measurements are reliable. For the curves in H = 0 and 0.01 T, however, the linear fittings give two negative values, κ 0 /T = − 0.24 and − 0.16 mW K −2 cm −1 , respectively. These negative κ 0 /T have no physical meaning, just because the temperature Scientific RepoRts | 6:21628 | DOI: 10.1038/srep21628 of our measurement is not low enough, comparing to the T c . Down to lower temperature, the curve in zero field should deviate from the linear behavior.
Since we can not extrapolate κ 0 /T at low field, we plot the field dependence of κ/T at T = 0.1 K, well below T c , in Fig. 4(b) to get more information about the superconducting gap structure of Ta 3 Pd 3 Te 14 31 . One can see that the increase of κ/T at low field is rather slow, and the curve is similar to that of dirty s-wave superconduting alloy InBi 32 , which is shown in Fig. 4(c). By using the estimated value of the coherence length ξ along b direction, the formula ξ = 0.18ħυ F /k B T c gives the Fermi velocity υ F = 5.11 × 10 4 m s −1 33 . Then, according to the relationship κ N0 /T = γ n υ F l e /3, the electron mean free path is estimated to be l e = 322 Å, which is much smaller than the b-direction ξ. This result indicates Ta 3 Pd 3 Te 14 is indeed in the dirty limit. Therefore, it is concluded that Ta 3 Pd 3 Te 14 is very likely a dirty s-wave superconductor.
It is instructive to compare the physical properties of the two structural closely related compounds of Ta 3 Pd 3 Te 14 and Ta 4 Pd 3 Te 16 , which we summarize in Table 1. Both of the two tellurides show Q1D characteristic with Q1D PdTe 2 chains. The larger RRR could account for the much sharper superconducting transition for Ta 3 Pd 3 Te 14 . Although T c of Ta 3 Pd 3 Te 14 is 3.6 K less than that of Ta 4 Pd 3 Te 16 , the former compound show much stronger electron correlations, verified by the larger renormalization factor and larger electron-nonphonon coupling strength λ nph . The small values of both Δ C/(γ n T c ) and λ ph indicate Ta 3 Pd 3 Te 14 is a weakly coupled superconductor. In addition, if assuming the Drude model, in which the electron-electron interactions are neglected, is applicable, a superconductor is expected to have a lower T c for a lower value of Sommerfield coefficient γ n , which in this case signifies the lower density of states at Fermi level. This simple conclusion is compatible with the general trend for the above two superconductors. Therefore, the lower T c in the title compound, may be attributed to the lower density of states at Fermi level. In this sense, by tuning the Fermi level of Ta 3 Pd 3 Te 14 or Ta 4 Pd 3 Te 16 by the way of doping or proper intercalations, the value of T c may be enhanced. By the way, in recently discovered PdTe or PdS chains based superconductors, there have been several pieces of work that show the evidences of two-gap SC 17,34,35 . However, our results presented above indicate the new superconductor Ta 3 Pd 3 Te 14 with PdTe 2 chains is very likely a fully gapped s-wave one. We have previously reported that Ta 4 Pd 3 Te 16 is possibly a two-gap superconductor with a gap symmetry of s + d waves 17 . Thus, if assuming the reduced part of electronic states at the Fermi level in Ta 3 Pd 3 Te 14 , compared to that in Ta 4 Pd 3 Te 16 , is primarily due to the reduced contribution from the Pd d states, it would be reasonable to see only a s-wave gap left in the former compound.

Methods
Powders of the elements Ta (99.97%), Pd (99.995%) and Te (99.99%) with a ratio of Ta : Pd : Te = 2 : 3 : 10 were thoroughly mixed together, loaded, and sealed into an evacuated quartz ampule. The sample-loaded quartz ampoule is then heated to 1223 K, held for 24 h, and cooled to 723 K at a rate of 5 K/h, followed by furnace cooling to room temperature. The above procedures are similar to that in growing Ta 4 Pd 3 Te 16 crystals 6 . The chemical composition is checked by an EDS with an AMETEK EDAX (Model Octane Plus) spectrometer, equipped in a field-emitting scanning electron microscope (SEM, Hitachi S-4800). It is worthy to mention that, although one may speculate the as-grown Ta 3 Pd 3 Te 14 crystals should be mixed by the Ta 4 Pd 3 Te 16 crystals in the same batch, our results do not support this speculation. The reasons are as follows: Using this method and atomic ratio of Ta : Pd : Te = 2 : 3 : 10 to grow Ta 3 Pd 3 Te 14 crystals, Ta 4 Pd 3 Te 16 crystals were occasionally harvested. However, our results show that the two kinds of crystals are never mixed with each other in the same batch. This conclusion is drawn by the fact that once the crystals, randomly picked up from the final product in one batch, are checked by both XRD and EDS to be Ta 3 Pd 3 Te 14 , not a single piece of Ta 4 Pd 3 Te 16 crystals can be identified in the same batch, and vise versa.
The magnetoresistance (MR) measurements were carried out in a 3 He cryostat down to 0.27 K by a stand four-probe technique with current applied along the b axis. The specific heat for a bundle of shiny needle-like crystals with a total mass m = 1.30(2) mg was measured by a long relaxation method utilizing a commercial 3 He microcalorimeter (Quantum Design PPMS-9). The thermal conductivity was measured in a commercial 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. The chemical composition of the crystals employed for above measurements have also been checked to be Ta 3 Pd 3 Te 14 by both XRD and EDS.