Pd3Te2: an s-wave superconductor with Pd atom coordinated by five Te atoms

We have identified a new superconductor Pd3Te2 based on pure phase samples. Electrical resistivity, magnetic susceptibility and specific heat measurements confirm that Pd3Te2 is a bulk superconductor at 2.2 K. The value of Ginzburg–Landau parameter is larger than 1/√2, suggesting type-II superconductivity. Meanwhile, the analysis of specific heat indicates that Pd3Te2 is a fully-gapped superconductor with electron-phonon coupling constant λe-p = 0.58, which features a BCS weakly coupling case. According to our theoretical calculations, the superconductivity is related to the states of hybridization of Pd d states and Te p states at the Fermi level. Our results reveal that superconductivity can occur in five coordinated palladium tellurides.


Introduction
Recently, palladium tellurides have been receiving considerable attention because of their structural diversity, superconducting and topological properties. These might be related with its unique electronic configuration (palladium has fewer electron shells being filled than its preceding elements) to some extent. For instance, Ta 4 Pd 3 Te 16 and Ta 3 Pd 3 Te 14 are quasi-one-dimension superconductors, which are composed of several different types of chains, including {PdTe 6 } octahedral chains [1,2]. Among the binary palladium tellurides, some also exhibit superconductivity [3]. Matthias showed that PdTe became a superconductor at about 2.3 K [4]. Later, it was found that the transition temperatures can be adjusted at a range of 1.8 K-4.5 K by slightly tuning the Te content in PdTe 1+x (0<x<0.08) [5][6][7]. PdTe has a three dimensional (3D) structure consisting of edge-sharing octahedral coordinated polyhedral {PdTe 6 }. The phase diagram of PdTe-PdTe 2 reported by Kjekshus et al confirmed that PdTe 2 is a superconductor with a T c of 1.69 K [8]. PdTe 2 is a layered compound forming by the stacking of layers composed of {PdTe 6 } octahedral as in PdTe. More recently, Noh et al reported the existence of type-II Dirac fermions in PdTe 2 by angle-resolved photoemission spectroscopy combined with ab initio band calculations [9].
Note that a common structural unit in Ta 4 Pd 3 Te 16 [1], Ta 3 Pd 3 Te 14 [2], PdTe [4] and PdTe 2 [8] is 6-coordinated {PdTe 6 } octahedral. It may play a vital role in inducing superconductivity in palladium tellurides. Pd 3 Te 2 , however, stands out for it comprises of two types of distorted {PdTe 5 } pyramids linked through edgeand corner-shared ways [10]. Besides, the topological surface states were predicted in Pd 3 Te 2 [11], which increases research interest. Since Pd 3 Te 2 is close to PdTe 1+x , PdTe 2 , and Pd 3 Te [3] in chemical compositions, it is difficult to synthesize pure phase and measure the intrinsic properties of Pd 3  of Pd 3 Te 2 has been obtained. In this paper, we have prepared a single phase of Pd 3 Te 2 through high-temperature (1173 K) melting and subsequent low-temperature (723 K) long-time (2 weeks) annealing treatment, which shows a superconducting transition with the 5-coordination at T c ∼2.2 K. The type II and s-wave superconductivity are confirmed by our magnetization and specific heat measurement. The derived electronphonon coupling indicates that it belongs to a BCS-type weakly-coupled superconductor.

Experimental
Polycrystalline samples of Pd 3 Te 2 were synthesized via the melting high purity palladium powder (99.99% Alfa Aesar) and tellurium powder (99.9999% Alfa Aesar). The powders of Pd and Te were weighted in the ratio of 3:2, thoroughly ground and pelleted. The pellet was packed into a corundum crucible, and sealed it into a quartz tube under vacuum, which was heated in a box furnace to 1173 K and held at this temperature for 30 h. Then the mixtures were ground to powder and were annealed in corundum crucibles for 2 weeks at about 723 K, which is to reduce the amount of PdTe as much as possible.
Powder x-ray diffraction (PXRD) patterns of the obtained sample were collected at room temperature using a Panalytical diffractometer with Cu K α (λ=1.5408 Å) radiation. Rietveld refinement of the PXRD patterns was performed using Fullprof software suites [13]. Microstructures of the Pd 3 Te 2 were examined using a scanning electron microscope (SEM). The chemical composition was determined by Energy Dispersive Spectrum (EDS) based on the average of five sets of data. The electrical resistivity (ρ), Hall effect and specific heat capacity (C p ) were measured through the standard four-wire method and the thermal relaxation method using the physical property measurement system with a He3 insert (PPMS, Quantum Design). The magnetic properties were characterized using a vibrating sample magnetometer (PPMS, Quantum Design). First principles calculations were performed with the Vienna ab-initio simulation package (VASP) [14,15]. We adopted the generalized gradient approximation (GGA) in the form of the Perdew-Burke-Ernzerhof (PBE) [16] exchange-correlation potentials. The projector augmented-wave (PAW) pseudopotential [17] was used with a plane-wave energy cutoff 600 eV. A Monkhorst-Pack [18] k-mesh of´14 14 6was used for sampling the first Brillouin zone in the self-consistent calculation and´27 27 13 for the density of states. Spin-orbital coupling effect was considered in the calculations. The lattice constants and atomic coordinates used in the calculations were derived from the experimental results.

Results and discussion
SEM images of small Pd 3 Te 2 crystals are shown in supplementary figure S1 is available online at stacks.iop.org/ JPCO/3/095008/mmedia. The chemical composition was determined as atomic ratio Pd:Te=3:2 within the measurement precision (±1% depending on the elements), confrming that the crystals is the stoichiometric Pd 3 Te 2 . The lattice parameters can be indexed as a=7.8994 (2) Å, b=12.6851 (3) Å, c=3.8551 (1) Å and V=386.305 (2) Å 3 . Figure 1 displays the Rietveld refinement of PXRD pattern of Pd 3 Te 2 powder sample. The observed reflections of main phase Pd 3 Te 2 obey the extinction conditions for space group Amam (No. 63). A two-phase Rietveld refinement [19] with initial structural prototype Pd 3 Te 2 [10] and PdTe converges well as R p =4.41%, R wp =6.34% and χ 2 =5.49. The mass fraction for main phase Pd 3 Te 2 and PdTe are 99% and 1%, respectively. Besides, the refined crystallographic parameters of Pd 3 Te 2 are shown in table 1. The crystal structure of Pd 3 Te 2 is shown in figure 2(a), which contains four formula units (f.u.) with 20 atoms in a unit cell. The structure of Pd 3 Te 2 is 3D structure comprising of two types of edge-and corner-shared {PdTe 5 } pyramids.  The temperature dependence of electrical resistivity (ρ) for Pd 3 Te 2 is shown in figure 4(a). Below 300 K, ρ(T) shows a metallic behavior with a linear dependence above 50 K. The high resistivity ratio (ρ 300 /ρ 0 ∼18) suggests that Pd 3 Te 2 is a good metal. The linear-dependence of Hall voltage against magnetic field (H) (see figure 3(a)) suggests that the Hall coefficient (R H ) is nearly independent of H. In figure 3(b), the positive value of R H over the entire temperature range (1.8-240 K) suggests that the conducting carriers are dominated by holes. This result reveals that its carrier type is opposite to those of PdTe and PdTe 2 [20,21]. With increasing temperature, R H increases slowly, and then the carriers concentration and carriers mobility decreases gradually, see The carrier concentration is estimated to be n=6×10 22 cm −3 at 240 K by n=1/eR H of the simple one-band model. Below 30 K, the R H decreases with lowering temperature to a minimum value of 4.4×10 −5 cm 3 C −1 , corresponding to n=1.4×10 23 cm −3 at 2 K.
A superconducting transition (T c onset ) is observed at 2.5 K and T c zero =2.2 K as shown in figure S2(a). There is no significant change in other temperature ranges, suggesting that the content of the residual of PdTe superconductivity phase is very small. Figure 4 , where Φ 0 =2.0678×10 9 Oe Å 2 [22], we can get the superconducting coherence length ξ 0 =513 (638) Å. The magnetic susceptibility is measured to further confirm the superconductivity of Pd 3 Te 2 . The magnetization is recorded in both zero field cooled (ZFC) and field cooled (FC) modes for Pd 3 Te 2 under H=10 Oe, which is shown in figure 4(d). Below 2.2 K, the susceptibility changes into negative value for both ZFC and FC curves. The 4πχ ZFC is about 60% at 1.8 K, because of demagnetizing field inside the material, indicating bulk superconductivity. We determined that the superconductivity of 2.2 K should come from the main phase of Pd 3 Te 2 rather than PdTe, because the mass fraction of PdTe is very small as our refined results. At the same time, we also found a weak superconducting transition (about 1%) at 4.5 K as shown in the figure S2(b), which is consistent with the report of superconductivity of PdTe in the literature [7,20]. Figure 4(e) shows the isothermal magnetization curves recorded from 1.8 K to 2.2 K in the superconducting state. As the magnetic field increase from zero, the absolute value of magnetization linearly decreases up to H c1 and then slowly increases. We are able to obtain H c1 at each temperature, and the estimation of     parameter κ is estimated to be 2.04 (2.10) by H c2 (0)=2 1/2 κH c (0), significantly larger than 1/gn, indicating a type-II superconductivity. Besides, the penetration depth λ(0) is found to be 1047 (1340) Å from λ(0)=κξ (0), which is larger than 786 Å of PdTe [20]. We measured the specific heat (C p ) of Pd 3 Te 2 from 2 K to 200 K, which is plotted in figure 5(a). The enlarged image of C p /T is shown in figure S2(c) from 0.2 K to 5 K, and the specific heat of samples 2 shows a slight jump at 4.3 K, which comes from the PdTe impurity. The experimental data cannot be well fitted by single Debye model. So we use an equation that includes the contribution of Einstein model to fit the data. The solid blue line is the fitting curve from the sum of Einstein and Debye model contributions,  Here, a is 0.90, R the gas constant, Θ D Debye temperature and Θ E Einstein temperature. Fitting the data against the above equation yields Θ D =217.2 K and Θ E =63.8 K. The inset of figure 5(a) shows the plot of C p /T versus T 2 . A sharp superconducting transition occurs at T c ∼2.2 K, in accordance with the transport data presented above. In the normal-state, the C p curve is well fitted by C p /T=γ+βT 2 +δT 4 from 3-10 K, where the first and the second term correspond to the normal-state electronic and phonon contribution, respectively. A linear fit to C p /T versus T 2 above T c gives the value of the Sommerfeld coefficient γ=9.67 mJ mol −1 K 2 , β=1.40 mJ mol −1 K 4 and δ=0.03 mJ mol −1 K 6 . Using the value of β, the Θ D can be calculated from the following expression [23]: where r=5 is the number of atoms per formula unit in Pd 3 Te 2 . We can obtain to the value of Θ D =191 K, which is close to the value of PdTe (203 K) [7]. By extrapolating the data in the superconducting state at zero field down to 0 K, we finds a residual value γ 0 ≈3.69 mJ mol −1 K 2 , indicating a contribution by a nonsuperconducting fraction in volume of about 38%. We suggest that the superconductivity depends sensitively on the stoichiometric ratio of Pd and Te. So, it is safe to conclude that the superconducting-state Sommerfeld coefficient (γ n ) for the present sample is 5.98 mJ mol −1 K 2 .
Using If the Coulomb parameter μ * is 0.13. The calculated λ e-p is 0.58, indicating a weak coupling state. We subtracted the phonon contribution from the C p and plotted the temperature-dependent electronic specific heat (C e ) over T from 0.2 K to 3.0 K in figure 5(b). The value for the jump, ΔC e /γ n T c , is 1.82 in the electronic specific heat at T c , which is higher than the BCS value (1.43) for superconductors in the weakcoupling limit. Such inconsistence in coupling state may come from an imprecise subtraction of the electronic contribution. Other Pd-Te superconductors are also reported to the BCS weak coupling state, like PdTe (1.33) [7], PdTe 2 (1.52) [25], Ta 4 Pd 3 Te 16 (1.4) [1] and Ta 3 Pd 3 Te 14 (1.35) [2]. The C e /T data (below 1/3 T c ) can be fitted by the expression from the BCS theory [23,26]. The yielded Δ(0)=0.176 meV. The good agreement between the measured data (green symbols) and the BCS fitting (blue line) provides evidence for an swave isotropic superconducting gap. Furthermore, the fitting yields Δ(0)/k B T c =1.12, which is also lower than the value of 1.76 for BCS theory.
The band structure, projected density of states and Fermi surface of Pd 3 Te 2 are shown in figure 6. The calculations were firstly checked for convergence, we choose 600 eV for cutoff energy and k-pacing 0.02 Å −1 (kmesh of 14×14×6), as shown in figure S3. We have calculated band structures with spin-orbital coupling. There are four bands crossing the Fermi level (E F ) along the high symmetry paths as shown in figure 6(a), the corresponding total and projected densities of states are shown in figure 6(b). The finite value of DOS at E F is consistent with the metallic behavior in ρ(T). The bands crossing E F are composed of hybridized states of Pd d and Te p orbitals. The each d-orbital contributions of Pd at the E F are almost equal, around 0.5/eV per primitive cell, while the each p-orbital of Te contributes ∼0.4/eV per primitive cell. The total DOS at E F is N(E F ) =5.61/ eV per primitive cell (2 formula units), corresponding to a value of electronic heat coefficient γ b =6.59 mJ mol −1 K 2 . According to the equation γ n =γ b (1+λ e-p )(mJ/mol K 2 ), we can obtain value γ n =10.41 mJ mol −1 K 2 , which is higher than the experimental value of 5.98 mJ mol −1 K 2 , because of nonsuperconducting phase of Pd 3 Te 2 sample. The Fermi surface of Pd 3 Te 2 has three-dimensional feature with rather complicated geometry, as shown in figure 6(c). The origin of superconductivity is dependent on Pd d states and Te p states at E F , irrelevant to atomic coordination in palladium tellurides system. All of the superconducting properties of Pd 3 Te 2 are listed in table 2.

Conclusion
In summary, we have investigated and studied the superconducting properties of polycrystalline Pd 3 Te 2 . The electrical resistivity, magnetic susceptibility and specific heat confirm that the T c of Pd 3 Te 2 is 2.2 K. Further analysis of the experimental data indicates that Pd 3 Te 2 is a type-II superconductor. The value of λ e-p suggests that the Pd 3 Te 2 is a BCS-type weakly-coupled superconductor. Our discovery reveals a new superconductor with 5-coordination in palladium tellurides system.