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/(γ(n)T(c)) ≈ 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 T(c), compared to that of Ta4Pd3Te16, may be attributed to the lower density of states.

Superconductivity (SC) in low-dimensional systems attracts sustained attention in SC community. The discovery of first layered cuprate superconductor (La, Ba)2CuO41, has set off a wave of exploring high-Tc superconductors. Since after, a number of new superconductors with low dimensional structures, such as quasi-two-dimensional (Q2D) strontium ruthenate2, ferroarsenides3, bismuth oxysulfides4, quasi-one-dimensional (Q1D) transition-metal chalcogenides5, ternary tellurides67, and newly discovered chromium-based compounds8, were reported to display the features of novel SC. The spin (charge) fluctuations910, strong electron-electron correlations11, or metal-insulator boundaries12 among low-dimensional systems constitute the newly strategic prerequisites to explore high-Tc superconductors. Generally, the presence of some transition metal elements among them, which bear strong electron correlations, are believed to play a significant role in producing the exotic pairing glue.

Owing to the inherent nature of transition metal chalcogenides13, the low-dimensional structures and rich physical properties, e.g., density-wave instability14, thermoelectricity15, and SC5, are prevalent among them. The tellurides, as compared with sulfides or selenides, are quite special in terms of its structures and properties because of the diffuse nature of the tellurium orbitals, and thus far rarely studied. Recently, we reported the observation of SC with T = 4.6 K in a ternary telluride Ta4Pd3Te16 with Q1D PdTe2 chains6. The detailed studies of its pairing symmetry were followed in applying the techniques of scanning tunneling microscopy16, low-temperature heat capacity17 and thermal conductivity18. The results indicate an anisotropic gap structure with the possible presence of nodes, although electronic structure calculations show the contributions of Pd 4d electrons to the density of states at Fermi level are pretty small19.

From a crystal-structure viewpoint, Ta4Pd3Te16 also belongs to a layered compound resulting from the condensation of Pd-based octahedral chains, Ta-based bicapped trigonal prismatic chains, and Ta-based double octahedral chains620. If the Ta-based double octahedral chains are replaced by Ta-based single octahedral chains, the condensation of the three different types of chains would form the atomic layer of a new compound Ta3Pd3Te14, which was firstly synthesized by Liimatta and Ibers in 198921. The major difference between them in structure is well reflected from Fig. 1(f), which shows the projection view of one atomic layer of Ta3Pd3Te14 and Ta4Pd3Te16 along the b axis. The structural details of Ta3Pd3Te14 are discussed below. Then, considering the close structural relationship of this material with the superconductor Ta4Pd3Te16, a natural question is whether the former is as well a superconductor.

Figure 1

Sample characterization and crystallographic structure of Ta3Pd3Te14.

(a) Morphology of a batch of the as-grown Ta3Pd3Te14 crystals under an optical microscope (left panel) and photographs of the crystals on a millimeter-grid paper (right panel). (b) Single-crystal X-ray diffraction pattern. The inset shows the third inflections in X-ray diffraction pattern for both Ta3Pd3Te14 and Ta4Pd3Te16. (c) A typical energy-dispersive X-ray spectrum with electron beams focused on the selected area (marked in the inset) of the crystals. A small amount of the element Al comes from the sample holder. (d) Crystal structure of Ta3Pd3Te14 projected along the [010] direction. An individual layer of Ta3Pd3Te14 is shown in the left panel of (e). The right panel of (e) is a piece of needle-like Ta3Pd3Te14 crystal under an optical microscope, from which the layered morphology can be clearly identified. (f) Projection view of one atomic layer of Ta3Pd3Te14 (left) and Ta4Pd3Te16 (right) along the b axis.

In this paper, we report the observation of SC with T = 1.0 K in layered ternary telluride Ta3Pd3Te14 with Q1D PdTe2 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 ΔC/(γT) ≈ 1.35 indicates Ta3Pd3Te14 may be a weakly coupled superconductor. In addition, the result of low-temperature thermal conductivity measurements of Ta3Pd3Te14 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 Ta3Pd3Te14 and Ta4Pd3Te16, and compiled an extended list of their physical properties.

Results

Single crystals of Ta3Pd3Te14 were grown using a self-flux method, rather than the vapor transport method previously used21. Shiny flattened needle-like crystals with a typical size of 2 × 0.15 × 0.1 mm3 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 ( 0 1) planes, consistent with the layered crystal structure of Ta3Pd3Te14. Ta3Pd3Te14 crystalizes in space group P21/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 K21. 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 ( 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 Ta3Pd3Te14 and Ta4Pd3Te16, 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 Ta3Pd3Te14 is ~2% smaller than that of Ta4Pd3Te16, 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 Ta3Pd3Te14 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) for the Ta3Pd3Te14 crystal (Sample 1). The larger room temperature resistivity (1.18 μΩ m), than that (0.61 μΩ m) of Ta4Pd3Te166, indicates Ta3Pd3Te14 is less conductive, consistent with the previous reports2122. The temperature dependence of resistivity shows a metallic behavior without any obvious anomaly down to T = 1.0 K, at which a sharp superconducting transition appears, as clearly depicted in Fig. 2(c). The value of T is 3.6 K less than that of Ta4Pd3Te16. The onset, midpoint, and zero-resistance temperatures are 1.02 K, 0.94 K, and 0.81 K, respectively, and the superconducting transition width ΔT is 0.13 K. The ρ(T) data between 2 and 25 K can be well fitted by to ρ = ρ0 + AT, giving a residual resistivity ρ0 = 5.13 μΩ cm and n = 2.83 [Fig. 2(b)]. The value of n more than 2 was also observed in Ta4Pd3Te16, which was attributed to the phonon-assisted s-d interband scattering18. The residual resistivity ratio (RRR) is estimated to be RRR = ρ(300 K)/ρ0 ~ 23, similar to that of Ta4Pd3Te16 (see Table 1).

Figure 2

Electrical transport and superconducting phase-diagram.

(a) Temperature dependence of electronic resistivity of Ta3Pd3Te14 crystal (Sample 1) along the b axis. (b) shows the power-law fit to ρ = ρ0 + AT in the data range of 2 and 25 K. (c) zooms into the low-temperature range to clearly show the superconducting transition. (d) The low-temperature resistivity in fields H || c* up to 0.1 T, from which the upper critical field (Hc2) is derived. (e) The red dashed line represents the Werthamer-Helfand-Hohenberg (WHH) fitting. (f) The extracted upper critical field Hc2 of Ta4Pd3Te16 crystal (Sample 2) for different field orientations.

Table 1

Comparison of some physical parameters of the superconductors Ta3Pd3Te14 (present work and20) and Ta4Pd3Te16 6171920.

Space group	Ta3Pd3Te14	Ta4Pd3Te16
	P21/m	I2/m
Physical parameters
RRR	23	26
Tc (K)	1.0	4.6
ΔTc (K)	0.13	0.76
(T/K) (H || c*)	−0.14	−0.44
μ0Hc2 (T) (H || c*)	0.075	3.3
γn (mJ mol−1 K−2)	28.2	46.1
θD (K)	151.6	148.8
λph	0.51	0.77
λnph	1.99	1.536, 0.1219
Nbs(EF) (eV−1 fu−1)	3.420	9.619, 5.520
ΔC/(γnTc)	1.35	1.40

RRR, T, ΔT, H, γ, θ, λph, λnph, Nbs(EF), and ΔC/(γT) 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.

Figure 2(d) plots the low-temperature resistivity of Ta3Pd3Te14 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 Hc2(T) for H || c*, determined by using 90% criterion, i.e., the field at which ρ 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 Hc223. As can be seen in Fig. 2(e), Hc2 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 λso = 1.2. However, by employing the orbital limiting field (0) = −0.69μ0 = 0.1 T in WHH model and the BCS Pauli-limiting field  = 1.84T = 1.84 T, the Maki parameter α = (0)/ 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 Ta3Pd3Te14. The extracted Hc2 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 Hc2 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 Ta4Pd3Te1617. The SC in Ta3Pd3Te14 is anisotropic but as well three-dimensional in nature, similar to other superconductors with Q1D characteristics, e.g., Ta4Pd3Te1617, Nb3Pd0.7Se724, and Nb2PdSe525, since the interchain coherence length and are much larger than the distance between two arbitrarily adjacent chains.

The low-temperature specific heat data of Ta3Pd3Te14 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 + βT2, which is represented as the red dashed line. The fitting yields an electronic heat capacity coefficient γ = 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 ΘD = 151.6 K is close to the value of Ta4Pd3Te16, consistent with the fact that the structures of two tellurides are closely related. However, the value of extracted coefficient γ is nearly 40% smaller than that of Ta4Pd3Te1617. Using the relation N(EF) =  for noninteracting electron systems, where kB is the Boltzmann constant, we estimated the density of states at the Fermi level N(EF) to be about 11.9 ± 0.8 eV−1 fu−1, which is 3.5 times that of the bare density of states Nbs(EF), obtained from the previous band-structure calculations20. Therefore, the larger renormalization factor [N(EF)/Nbs(EF) = 1 + λ], than that for Ta4Pd3Te16, suggests much stronger electron-electron correlations in Ta3Pd3Te14, although the recent band-structure calculations are concluded with a higher Nbs(EF) = 9.6 eV−1 fu−1 for Ta4Pd3Te16, thus resulting in a much lower renormalization factor19. To extract the electron-nonphonon coupling strength λnph in λ, we estimate the electron-phonon coupling constant λph by employing the McMillan formula26, λph = [1.04 + μ*ln(ΘD/1.45T)]/[(1 − 0.62μ*)ln(ΘD/1.45T) − 1.04], where the Coulombic repulsion parameter μ* is empirically set to be 0.13. The estimated value of λph is 0.51, a little bit smaller than that of the superconductor Ta4Pd3Te166. However, the resultant constant λnph = λ − λph = 1.99 is much larger than that of Ta4Pd3Te16, possibly indicating much larger electron correlations in the former compound.

Figure 3

Temperature dependence of specific heat.

(a) C/T vs T, in which the red dashed line represents the fit with the formula C/T = γ + βT2 for the normal-state data from 1.2 to 6.5 K. (b) The electronic specific heat divided by temperature Cel/T in the superconducting state, where Cel = C − βT 3.

Discussion

We discuss the electronic heat capacity Cel of Ta3Pd3Te14 crystals in low-temperature range, obtained by Cel = C − βT 3. As can be seen in Fig. 3(b), a characteristic superconducting jump (ΔCel) shows up around ~1 K, confirming the bulk SC. The ΔCel/T 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 Ta3Pd3Te14 may be a weakly coupled superconductor. Unfortunately, due to the insufficient data points, we are unable to fit ΔCel(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 Ta3Pd3Te14 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 Ta4Pd3Te1618 and some iron-based superconductors2728, we fit all the curves to κ/T = a + bT by fixing α to 2. The two terms aT and bT represent contributions from electrons and phonons, respectively2930. From the curve in magnetic field H = 0.09 T, which is close to the critical field H(0) for || c*, one can see that the obtained κ0/T roughly meets the normal-state Wiedemann-Franz law expectation κN0/T = L0/ρ0 = 2.44 mW K−2 cm−1. Here, L0 is the Lorenz number 2.45 × 10−8 W Ω K−2 and ρ0 = 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, κ0/T = −0.24 and −0.16 mW K−2 cm−1, respectively. These negative κ0/T have no physical meaning, just because the temperature of our measurement is not low enough, comparing to the T. Down to lower temperature, the curve in zero field should deviate from the linear behavior.

Figure 4

Low-temperature thermal conductivity data.

(a) Low-temperature thermal conductivity of Ta3Pd3Te14 crystal (Sample 2) in zero and magnetic fields applied along c* direction. The dashed lines are fits to the formula κ/T = κ0/T + bT. The black dashed line is the normal-state Wiedemann-Franz law expectation L0/ρ0. (b) The field dependence of κ/T at 0.1 K. (c) Normalized residual linear term κ0/T as a function of normalized field H/H for the clean s-wave superconductor Nb36, the dirty s-wave superconducting alloy InBi32, the multi-band s-wave superconductor NbSe237, and an overdoped d-wave cuprate superconductor Tl-220138.

Since we can not extrapolate κ0/T at low field, we plot the field dependence of κ/T at T = 0.1 K, well below T, in Fig. 4(b) to get more information about the superconducting gap structure of Ta3Pd3Te1431. 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 InBi32, 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/kT gives the Fermi velocity υ = 5.11 × 104 m s−1 33. Then, according to the relationship κN0/T = γυl/3, the electron mean free path is estimated to be l = 322 Å, which is much smaller than the b-direction ξ. This result indicates Ta3Pd3Te14 is indeed in the dirty limit. Therefore, it is concluded that Ta3Pd3Te14 is very likely a dirty s-wave superconductor.

It is instructive to compare the physical properties of the two structural closely related compounds of Ta3Pd3Te14 and Ta4Pd3Te16, which we summarize in Table 1. Both of the two tellurides show Q1D characteristic with Q1D PdTe2 chains. The larger RRR could account for the much sharper superconducting transition for Ta3Pd3Te14. Although T of Ta3Pd3Te14 is 3.6 K less than that of Ta4Pd3Te16, the former compound show much stronger electron correlations, verified by the larger renormalization factor and larger electron-nonphonon coupling strength λnph. The small values of both ΔC/(γT) and λph indicate Ta3Pd3Te14 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 for a lower value of Sommerfield coefficient γ, 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 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 Ta3Pd3Te14 or Ta4Pd3Te16 by the way of doping or proper intercalations, the value of T 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 SC173435. However, our results presented above indicate the new superconductor Ta3Pd3Te14 with PdTe2 chains is very likely a fully gapped s-wave one. We have previously reported that Ta4Pd3Te16 is possibly a two-gap superconductor with a gap symmetry of s + d waves17. Thus, if assuming the reduced part of electronic states at the Fermi level in Ta3Pd3Te14, compared to that in Ta4Pd3Te16, 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 Ta4Pd3Te16 crystals6. 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 Ta3Pd3Te14 crystals should be mixed by the Ta4Pd3Te16 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 Ta3Pd3Te14 crystals, Ta4Pd3Te16 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 Ta3Pd3Te14, not a single piece of Ta4Pd3Te16 crystals can be identified in the same batch, and vise versa.

The magnetoresistance (MR) measurements were carried out in a 3He 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 3He 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 RuO2 chip thermometers, calibrated in situ against a reference RuO2 thermometer. The chemical composition of the crystals employed for above measurements have also been checked to be Ta3Pd3Te14 by both XRD and EDS.

Additional Information

How to cite this article: Jiao, W.-H. et al. Superconductivity in Ta3Pd3Te14 with quasi-one-dimensional PdTe2 chains. Sci. Rep. 6, 21628; doi: 10.1038/srep21628 (2016).