Superconductivity in REO_0.5F_0.5BiS₂ with high-entropy-alloy-type blocking layers

Since the discovery of the cuprate superconductors and FeAs-based superconductors,^1,2) layered compounds have been extensively studied as a potential system in which high-transition-temperature (high-T_c) superconductivity and unconventional mechanisms of superconductivity emerge. Basically, layered superconductors have a structure based on alternate stacks of electrically conducting layers, such as the CuO₂ layer and FeAs layer, and insulating (blocking) layers, which are typically composed of metal oxides.

In 2012, we discovered new layered superconductors with BiS₂-based conducting layers.^3–5) Basically, the parent phase of the BiS₂-based superconductors is a semiconductor with a band gap.^6,7) When electron carriers are generated in the BiS₂ layers, superconductivity emerges. In the typical system LaO_1−xF_xBiS₂, the carrier amount can be controlled by the composition of F (x) in the LaO blocking layer.⁴⁾ Since the discovery in 2012, many BiS₂-based superconductors with different types of blocking layer have been synthesized, for which T_c is largely enhanced by replacing (or partially substituting) elements in the blocking layer.⁵⁾ In particular, as reported in Refs. 8 and 9, the relationship between the superconducting properties and the crystal structure has been systematically studied by tuning the chemical pressure effect in the REO_0.5F_0.5BiS₂ system, where the average ionic radius of the RE site was systematically changed with the solution of La, Ce, Pr, Nd, or Sm. Based on these investigations on chemical pressure effects, we found that both carrier doping and the optimization of the local structure (particularly the suppression of in-plane disorder of the BiS plane) were essential for the emergence of bulk superconductivity in the BiS₂-based superconductors.^8–12)

The chemical pressure effect in REO_0.5F_0.5BiS₂ is basically controlled by the alloying effect at the RE site of the blocking layer. The systematic shrinkage of the blocking layer affects the Bi–S1 (S1 is an in-plane sulfur as depicted in the inset of Fig. 1.) bond distance and induces bulk superconductivity. This fact suggests that the structural properties of the RE(O,F) blocking layer affect the superconducting properties in the RE(O,F)BiS₂ system. Furthermore, if the structural stability of the RE(O,F) blocking layer is enhanced, the superconducting properties may increase in RE(O,F)BiS₂. To investigate this possibility, we have studied the crystal structure and the superconducting properties of (La,Ce,Pr,Nd,Sm)O_0.5F_0.5BiS₂, where the (La,Ce,Pr,Nd,Sm)O_0.5F_0.5 layer was designed with the concept of a high entropy alloy (HEA), which has been proposed as a promising strategy for designing novel functional materials.¹³⁾

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Typically, an HEA is defined as an alloy containing at least five elements with concentrations between 5 and 35 atomic percent, according to the paper by Yeh et al.¹⁴⁾ Furthermore, Otto et al. suggested that only an alloy that forms a solid solution with no intermetallic phases should be considered as an HEA, because the formation of an ordered phase decreases the entropy of the system.¹⁵⁾ Recently, Koželj et al. discovered superconductivity in Ta₃₄Nb₃₃Hf₈Zr₁₄Ti₁₁ with T_c of 7.3 K.¹⁶⁾ The observed superconductivity in the HEA was conventional phonon-mediated superconductivity. Notably, high-pressure measurements revealed that the superconductivity (zero-resistivity state) in the HEA superconductor was robust at pressures up to 190 GPa.¹⁷⁾ This fact suggests that the superconducting states of the HEA can be enhanced by the HEA effect under extreme conditions.

On the basis of the observed structural stability in the HEA superconductor under extremely high pressure, we expected that the local disorder in RE(O,F)BiS₂, which negatively affects the emergence of bulk superconductivity, can be suppressed, and the superconducting properties may be enhanced by the HEA effect. However, RE(O,F)BiS₂ is a layered system and composed of five different atomic sites, in which a simple HEA concept cannot be applied. Therefore, we focused on the RE site (see the inset of Fig. 1) only and designed the HEA-type RE(O,F) blocking layers as a solid solution of RE = La, Ce, Pr, Nd, and Sm. In this letter, four HEA-type REO_0.5F_0.5BiS₂ samples were newly synthesized. Powder X-ray diffraction (XRD) and Rietveld refinements revealed that the obtained HEA-type REO_0.5F_0.5BiS₂ is almost single-phase and structurally homogeneous as in the other typical REO_0.5F_0.5BiS₂ (RE = La, Ce, Pr, and Nd), where the RE site consists of one or two RE elements. For all the HEA-type REO_0.5F_0.5BiS₂ samples, a sharp superconducting transition was observed. Notably, we observed that the superconducting phase diagram of HEA-type REO_0.5F_0.5BiS₂ showed a trend clearly different from that of typical REO_0.5F_0.5BiS₂. Although only the RE site possesses an HEA state in HEA-type REO_0.5F_0.5BiS₂, the superconducting properties seem to be enhanced as compared with typical REO_0.5F_0.5BiS₂. Hence, the concept of designing layered superconductors with an HEA-type blocking layer will provide us with a new strategy for synthesizing new layered superconductors with outstanding properties.

We synthesized four REO_0.5F_0.5BiS₂ superconductors with nominal compositions of La_0.3Ce_0.3Pr_0.2Nd_0.1Sm_0.1O_0.5F_0.5BiS₂, La_0.2Ce_0.2Pr_0.2Nd_0.2Sm_0.2O_0.5F_0.5BiS₂, La_0.1Ce_0.1Pr_0.3Nd_0.3Sm_0.2O_0.5F_0.5BiS₂, and La_0.1Ce_0.1Pr_0.2Nd_0.3Sm_0.3O_0.5F_0.5BiS₂, which are labeled as A, B, C, and D, respectively. The polycrystalline samples were synthesized by the solid-state-reaction method similar to that established for typical REO_0.5F_0.5BiS₂.^4,8) Powders of La₂S₃ (99.9%), Ce₂S₃ (99.9%), Pr₂S₃ (99.9%), Nd₂S₃ (99%), Sm₂S₃ (99.9%), Bi₂O₃ (99.999%), and BiF₃ (99.9%) and grains of Bi (99.999%) and S (99.99%) were used as starting materials. The mixture of the starting materials listed above with the nominal composition was mixed well, pelletized, sealed into an evacuated quartz tube, and heated at 700 °C for 20 h. The obtained sample was ground, mixed, pelletized, sealed into an evacuated quartz tube, and heated at 700 °C for 20 h to homogenize the sample.

The phase purity and the crystal structure were examined using powder XRD with Cu Kα radiation by the θ–2θ method. Rietveld refinements were performed to analyze the obtained XRD data. The RIETAN-FP software was used for the Rietveld analysis.¹⁸⁾ To visualize the refined crystal structure, the VESTA software was used.¹⁹⁾ The actual composition for the RE site was analyzed using energy-dispersive X-ray spectrometry (EDX). As listed in Table S1 in the online supplementary data at http://stacks.iop.org/APEX/11/053102/mmedia, the analyzed RE concentrations almost corresponded to the nominal values for all the samples. Therefore, in this paper, we describe the sample names using the nominal values for clarity.

The temperature dependence of the electrical resistivity was measured by the four-terminal method with a current of 1 mA. The temperature dependence of the magnetic susceptibility was measured by a superconducting quantum interference device (SQUID) magnetometer after both zero-field cooling (ZFC) and field cooling (FC) with a typical applied field of 10 Oe.

Figure 1 shows the typical XRD pattern and the Rietveld fitting result for sample B (La_0.2Ce_0.2Pr_0.2Nd_0.2Sm_0.2O_0.5F_0.5BiS₂). Although tiny impurity peaks probably due to RE₂O₂S were observed, almost all the peaks were refined using the tetragonal P4/nmm model.⁴⁾ See the online supplementary data at http://stacks.iop.org/APEX/11/053102/mmedia for the Rietveld refinement results for A, C, and D. For sample B, as shown in the inset of Fig. 1, the RE site can be regarded as an HEA type with La, Ce, Pr, Nd, and Sm with a concentration of 19–21%, which satisfies the definition of the HEA by Yeh et al.¹⁴⁾ For other samples A, C, and D, high purity of the obtained samples was also confirmed by the Rietveld refinements. The obtained crystal structure parameters are listed in Tables S1 and S2 in the online supplementary data at http://stacks.iop.org/APEX/11/053102/mmedia. Changing the RE concentration from A to D does not affect the structural model with the P4/nmm space group but systematically decreases the lattice constant a as shown in Fig. 2. This trend is similar to that in the case of Ce_1−xNd_xO_0.5F_0.5BiS₂ or other related systems.^8,9) Generally, in the REOBiS₂-type compounds, the lattice expansion/shrinkage is directly linked to the mean ionic radius of the RE site.^8,9) However, the lattice constant c for the HEA samples increases from A to D. On the basis of previous works, we have found the trend that the lattice constant c of the REOBiS₂-type compounds decreases with increasing carrier concentration.^4,8) Therefore, the increase in c for samples C and D may be related to the decrease in the electron carrier concentration. In samples C and D, the Sm concentration is larger than that in the samples A and B. This may indicate that the Sm ions are in the mixed-valence state of +2 and +3, as observed in other Sm compounds.²⁰⁾ In addition, in the plot the lattice constant a for the HEA-type samples is clearly larger than that for typical REO_0.5F_0.5BiS₂, which also suggests that the RE ionic radius for any RE site is larger than that of RE³⁺. The in-plane Bi–S1 distance decreases with decreasing a. The S1–Bi–S1 angle is almost 180° and does not show a marked change between A, B, C, and D. Therefore, with decreasing Bi–S1 distance, in-plane chemical pressure is generated without any change in the flatness of the BiS1 plane.⁹⁾

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Regarding the homogeneity of the HEA-type samples, there is the possibility of local phase separation into grains with different RE ions. However, as shown in Fig. 2(c), the typical peak (110 reflection) for the HEA-type samples is not broadened by mixing five RE elements and seems slightly sharper than that of typical systems with RE = La and Nd. In addition, the full width at half maximum (FWHM) of the 110 peak plotted in Fig. 2(d) shows that the peak sharpness for the HEA-type samples is narrower than that for typical REO_0.5F_0.5BiS₂ (RE = La and Nd). We consider that the RE ions are homogeneously solved in the grains on the basis of the present powder XRD study. Furthermore, the REO_0.5F_0.5BiS₂ structure may be stabilized by the HEA effect.

Figure 3(a) shows the temperature dependences of the electrical resistivity for A–D. For all the samples, the resistivity above T_c increases with decreasing temperature, which is a semiconducting-like behavior. In several BiS₂-based superconductors, a similar behavior was observed.^4,5) In typical REO_0.5F_0.5BiS₂, the semiconducting behavior was suppressed with increasing in-plane chemical pressure.^10,21) In addition, in LaO_0.5F_0.5BiS_2−xSe_x, which is the best example showing a dramatic in change the in-plane chemical pressure amplitude, the increase in the in-plane chemical pressure (Se concentration) induced metallic conductivity and bulk superconductivity.^10,21) Although the temperature dependences of the resistivity are similar for all the present samples A–D, we notice that the increase in resistivity at low temperatures for samples C and D is weaker than that for A and B in the plot of normalized resistivity [Fig. 3(b)].

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Figure 3(c) shows the low-temperature resistivity plots. For all the samples, a sharp superconducting transition was observed. The onset temperature ($T_{\text{c}}^{\text{onset}}$) was defined as the temperature where the resistivity begins to decrease upon cooling. $T_{\text{c}}^{\text{zero}}$ was defined as the temperature where the resistivity becomes zero upon cooling. The estimated $T_{\text{c}}^{\text{onset}}$ is 3.4, 4.3, 4.7, and 4.9 K for A, B, C, and D, respectively. The estimated $T_{\text{c}}^{\text{zero}}$ is 3.0, 3.8, 4.2, and 4.5 K for A, B, C, and D, respectively. The transition width (ΔT_c) estimated from the difference between $T_{\text{c}}^{\text{onset}}$ and $T_{\text{c}}^{\text{zero}}$ is 0.4, 0.5, 0.5, and 0.4 K, for A, B, C, and D, respectively. The sharpness of the transition for the present sample is sharper than that of typical REO_0.5F_0.5BiS₂; for example, ΔT_c of PrO_0.5F_0.5BiS₂ is ∼0.8 K according to the temperature derivative of the resistivity in Ref. 22. In typical REO_0.5F_0.5BiS₂ systems, the existence of strong superconducting fluctuations has been proposed.²³⁾ Furthermore, structural instability, due to the presence of the lone-pair effect of the Bi 6s electrons,¹¹⁾ also exists in the typical REO_0.5F_0.5BiS₂ system,^4,5,24) which is linked to the emergence of bulk superconductivity. These superconducting fluctuations or the structural instabilities can broaden the superconducting transition. On the basis of the discussion above, we propose that the HEA-type blocking layer may suppress these fluctuations and structural instabilities and induce the sharp superconducting transition.

Figure 3(d) shows the temperature dependences of the magnetic susceptibility 4πχ for A, B, C, and D. For all the samples, diamagnetic signals due to the emergence of superconductivity were observed. The transition temperature $T_{\text{c}}^{\text{mag}}$, estimated as the temperature where the susceptibility begins to drop, is 3.1, 3.8, 4.2, and 4.4 K for A, B, C, and D, respectively. $T_{\text{c}}^{\text{mag}}$ almost corresponds to $T_{\text{c}}^{\text{zero}}$ estimated from the resistivity data. For C and D, a large shielding fraction was observed, suggesting the emergence of bulk superconductivity in the HEA-type REO_0.5F_0.5BiS₂ samples. The magnetization loop for sample D is shown in the online supplementary data at http://stacks.iop.org/APEX/11/053102/mmedia. We confirmed that the superconducting states in the HEA-type samples are also robust to the magnetic field. In the typical REO_0.5F_0.5BiS₂ systems, the shielding volume fraction is enhanced with increasing transport metallicity.^5,10,21) Therefore, although the suppression is slight, as shown in Fig. 3(b), the larger shielding fraction in C and D than that of A and B may be related to the suppression of carrier localization.

Here, we discuss the evolution of T_c and shielding fraction [using Δ4πχ calculated by 4πχ(FC) − 4πχ(ZFC) at 2 K] as a function of the lattice constant a. As mentioned above, the flatness of the BiS1 plane is almost the same for all the samples including typical REO_0.5F_0.5BiS₂ with RE = La, Ce, Pr, and Nd [plotted in Figs. 3(e) and 3(f) for comparison]. Therefore, the lattice constant a can be a good indicator to discuss the shrinkage (in-plane chemical pressure) amplitude of the superconducting BiS1 plane. In Figs. 3(e) and 3(f), the dependences of T_c and Δ4πχ as a function of lattice constant a are respectively plotted with the data of REO_0.5F_0.5BiS₂ (RE = La, Ce, Pr, and Nd) and the solid-solution systems with RE = La_1−xCe_x and Ce_1−xNd_x.^4,8,12) The T_c plot for the HEA-type samples (A, B, C, and D) is slightly higher than that for typical REO_0.5F_0.5BiS₂. Δ4πχ for B, C, and D is close to that for RE = Pr and Nd. However, Δ4πχ for A is notably larger than that expected from the dependence of typical REO_0.5F_0.5BiS₂ phases. These results may indicate that the HEA-type blocking layer positively affects the superconducting states emerging in the BiS₂ layers. Probably, in-plane disorder is suppressed by the stabilization of the crystal structure by the HEA effect in REO_0.5F_0.5BiS₂. To obtain evidence for the positive link, we will investigate the local crystal structure using synchrotron XRD and X-ray absorption spectroscopy as carried out on the typical BiS₂-based superconductor system.^9–12)

In conclusion, we newly synthesized four superconducting phases, La_0.3Ce_0.3Pr_0.2Nd_0.1Sm_0.1O_0.5F_0.5BiS₂, La_0.2Ce_0.2Pr_0.2Nd_0.2Sm_0.2O_0.5F_0.5BiS₂, La_0.1Ce_0.1Pr_0.3Nd_0.3Sm_0.2O_0.5F_0.5BiS₂, and La_0.1Ce_0.1Pr_0.2Nd_0.3Sm_0.3O_0.5F_0.5BiS₂, whose blocking layer has been designed with the HEA concept. The lattice constant a systematically changed in the four samples with the RE concentration and the RE ionic radius. For all the samples, a superconducting transition was observed. Notably, the superconducting transition in the resistivity–temperature plot was quite sharp (sharper than that of typical PrO_0.5F_0.5BiS₂). The sharp transition may indicate that the superconductivity fluctuations and/or the structural instability^4,11,23,24) are suppressed by the HEA effect. The plot of T_c as a function of lattice constant a for the HEA-type samples was higher than those of typical REO_0.5F_0.5BiS₂. Furthermore, for sample A (with a large lattice constant a), the observed shielding volume fraction estimated from the susceptibility data was clearly higher than that expected from the trend in typical REO_0.5F_0.5BiS₂. The enhancement of the superconducting properties observed in the HEA-type samples may be related to the HEA effect in the blocking layer. We believe that the introduction of the HEA effects into the blocking layers of layered superconductors will be a useful strategy to improve the superconducting properties such as T_c, upper critical field, and critical current density.

Acknowledgments