Robustness of Superconductivity to External Pressure in High-Entropy-Alloy-Type Metal Telluride AgInSnPbBiTe5

Robustness of Superconductivity to External Pressure in High-Entropy-Alloy-Type Metal Telluride AgInSnPbBiTe5 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Robustness of Superconductivity to External Pressure in High-Entropy-Alloy-Type Metal Telluride AgInSnPbBiTe 5 Yoshikazu Mizuguchi, Riad Kasem, Yuki Nakahira, Hitoshi Yamaoka, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1319304/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract High-entropy-alloy (HEA) superconductors are a new class of disordered superconductors. However, commonality of superconducting characteristics of HEA materials is unclear. Here, we have investigated the crystal and electronic structure, and the robustness of superconducting states in a HEA-type metal telluride ( M Te; M = Ag, In, Sn, Pb, Bi) under high pressure, and the results were compared with the pressure effects for a middle-entropy system (AgPbBiTe 3 ) and a reference system of PbTe. When the crystal structure is CsCl-type, all phases show superconductivity under high pressure but exhibit different pressure dependences of the transition temperature ( T c ). For PbTe, its T c decreases with pressure. In contrast, the T c of HEA-type AgInSnPbBiTe 5 is almost independent of pressure, for pressures ranging from 13.0 to 35.1 GPa. Those results suggest that the robustness of superconductivity to external pressure is linked to the configurational entropy of mixing at the M site in M Te. Since the trend is quite similar to previous work on a HEA (Ti-Zr-Hf-Nb-Ta), where the robustness of superconductivity was observed up to ~ 200 GPa, we propose that the robustness of superconductivity under high pressure would be a universal feature in HEA-type superconductors. Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The superconductivity of disordered materials has been extensively studied because of an observation made on the insulator-superconductor transition or disorder-induced superconductivity [ 1 – 3 ]. In addition, recent studies on BiS 2 -based layered superconductors have shown the importance of controlling the local structural disorder to improve superconducting properties [ 4 – 7 ]. As a new category of disordered superconductors, high-entropy alloys (HEAs), which are alloys containing five or more elements with an atomic concentration between 5% and 35% [ 8 , 9 ], have been extensively studied, leading to the discovery of a wide range of HEA superconductors [ 10 – 12 ]. One of the notable features is the difference in characteristics of superconductivity among conventional metal or alloy superconductors, superconducting thin films, and HEA superconductors [ 11 , 13 ]. Furthermore, the robustness of superconductivity to extremely high pressure (HP), for pressures up to 190 GPa, in an HEA, (TaNb) 0.67 (HfZrTi) 0.33 , was observed [ 14 ]. The high configurational entropy of mixing (Δ S mix ) reduces the Gibbs’s free energy, and therefore stabilization of the phase is expected. The equation for calculating the Gibb’s free energy is Δ G = Δ H - T Δ S mix, where Δ H is the enthalpy and T is the absolute temperature. Δ S mix can be calculated using the equation Δ S mix = - R ∑ i c i ln c i , where, R is the gas constant and c i is the atomic ratio of the element ( i ) [ 8 ]. The discovery of the robustness of superconductivity under an extremely high pressure was considered to be related to the high Δ S mix , but similar robustness of superconductivity under an extremely high pressure and a high transition temperature ( T c ) of 19 K was observed in a low-entropy Nb-Ti alloy [ 15 ]. Therefore, the effects of Δ S mix on the crystal structure, electronic structure, and superconducting properties of HEAs are still unclear. To address this issue, further investigation of HP effects on HEA-type materials is needed. We recently developed superconducting HEA-type compounds, in which one of the crystallographic sites is alloyed with the criterion similar to HEAs [ 16 ]. Since compounds with two or more crystallographic sites have unique chemical bonds, various (novel) effects of the introduction of HEA site to electronic and structural properties would be expected, which is so-called cocktail effect in the field of HEAs. In the layered BiS 2 -based superconductor RE (O,F)BiS 2 , the rare-earth site ( RE ) was alloyed with five different RE elements [ 17 ], and the improvement of superconducting properties (bulk nature of superconductivity) with increasing Δ S mix was observed [ 18 ]. T c was not affected by Δ S mix , and therefore its insensitivity to Δ S mix in the BiS 2 -based superconductor is explained using a two-dimensional structure, since similar insensitivity was also observed in an RE 123 cuprate with an HEA-type RE site [ 19 ]. In contrast, T c of NaCl-type metal telluride, which is the target phase of this study, shows that its sensitivity to Δ S mix of HEA-type systems is larger than that of metal tellurides with one or two constituent elements at the metal site [ 20 , 21 ]. On the basis of the facts described above, we considered that the metal telluride system is suitable for the discussion of the effects of high Δ S mix on the crystal structure (phase stability) and superconducting properties under high pressure. Here, we studied the crystal structure, electronic structure, and superconducting properties of three tellurides ( M Te; M = Ag, In, Sn, Pb, Bi) with different Δ S mix values at the M site: PbTe (Δ S mix = 0), AgPbBiTe 3 (Δ S mix = 1.1 R ), and AgInSnPbBiTe 5 (Δ S mix = 1.6 R ). The pressure evolutions of the crystal structure and electronic transport properties were reported in previous studies [ 22 – 26 ]. Although PbTe is a semiconductor under ambient and low pressures, it undergoes metallization under high pressures, and a superconducting transition is observed for pressures above 15 GPa [ 22 , 23 ]. PbTe undergoes structural transitions as follows: cubic NaCl-type ( Fm -3 m ) structure under low pressures, orthorhombic ( Pnma ) structure under moderate pressures, and cubic CsCl-type ( Pm -3 m ) structure under HP [ 24 – 26 ]. There is a report on synthesis and thermoelectric properties of AgPbBiTe 3 , but the structural and physical properties of AgPbBiTe 3 have not been reported [ 27 ]. In this study, we established a phase diagram of the crystal structures, as well as one for superconductivity versus pressure for both AgPbBiTe 3 and AgSnInPbBiTe 5 . We also studied PbTe to examine the effects of configurational entropy of mixing. The pressure phase diagrams for the three tellurides are used to compare the crystal and electronic structures in detail. The results show that the pressure phase diagram of the crystal structure is largely modified by the effect of Δ S mix . Furthermore, we found that the pressure dependence of T c in the HP phase (CsCl-type phase) exhibits a clear difference among the three compounds. In the HP phase, the T c for PbTe decreases with pressure, but that for HEA-type AgInSnPbBiTe 5 exhibits a flat dependence, which suggests that the superconducting state of AgInSnPbBiTe 5 is robust to pressure. Our present findings show an analogical conclusion in the case of (TaNb) 0.67 (HfZrTi) 0.33 [ 14 ] and suggest that the HEA effects universally enhance the robustness of superconductivity under high pressure. 2. Results 2.1. Electrical resistance Figure 1 a shows the temperature dependence of the electrical resistance of AgInSnPbBiTe 5 measured using the conventional four-probe method at ambient pressure. T c zero was 1.8 K, which is slightly lower than that reported in previous research [ 20 ]. We measured the electrical resistance (at National Institute for Materials Science) after several days since the sample was synthesized by HP annealing (at Tokyo Metropolitan University), and a slight aging effect of T c was noticed in M Te superconductors synthesized under high pressure [ 28 , 29 ]. We consider that the slight decrease in T c can be understood by the change in the internal strains because the XRD patterns do not show a remarkable change after aging in the HP-synthesized M Te samples. Therefore, we continued to perform resistance measurements under high pressure using a diamond-anvil cell (DAC). Figure 1 b shows the temperature dependences of the electrical resistance of AgInSnPbBiTe 5 measured under various pressures with a DAC. Normal-state resistance decreases with pressure, for pressures up to 9.3 GPa and increases with pressure for pressures above 15.5 GPa. An onset of the superconducting transition was observed at 2 K under 6.5 GPa, and the zero-resistance state was observed at T c zero = 2 K under 10.2 GPa. As shown in Fig. 2 a, the T c onset monotonously increased with pressure until it reached 13.0 GPa, and then it became insensitive to pressure for pressures ranging from 13.0 GPa to 35.1 GPa ( P = 35.1 GPa is the chosen maximum pressure for the experiment). The results indicate that the T c in the CsCl-type structure of AgInSnPbBiTe 5 is independent of applied pressure, while lattice constant decreases with pressure. The highest T c zero and T c onset observed in the experiment on AgInSnPbBiTe 5 are 4.5 K and 5.3 K, respectively. See Figure S1 for the determination criterion for T c onset . To compare the pressure evolution of T c in AgInSnPbBiTe 5 with that of PbTe and AgPbBiTe 3 , the pressure dependences of T c onset for PbTe and AgPbBiTe 3 were examined (see Fig. 2 c for structural difference and Figs. S2 and S3 for the resistance measurements), and the resulting T c - P plots are shown in Fig. 2 b. PbTe is a semiconductor at ambient and low pressures, but exhibits a pressure-induced superconducting transition above 17 GPa in the CsCl-type structure [ 22 ]. At higher pressures, T c of PbTe monotonously decreases with pressure. In the case of AgPbBiTe 3 , superconductivity was observed at P > 2.6 GPa, and at this instance T c onset reached 6.5 K. The T c for AgPbBiTe 3 slightly decreases at high pressures. In AgInSnPbBiTe 5 , superconductivity is observed at low pressures as well because the low-pressure phase, having a NaCl-type structure, itself is a metal and shows superconductivity under ambient pressure (Figs. 1 a and 2 a). As demonstrated in the next section, the crystal-structure type under high pressure is CsCl-type for all the compounds. However, the trend of the pressure dependences of T c in the CsCl-type structure exhibit a clear difference among PbTe, AgPbBiTe 3 , and AgInSnPbBiTe 5 . The main findings of this study are that the robustness of superconductivity to pressure in HEA-type AgInSnPbBiTe 5 is similar to that observed in (TaNb) 0.67 (HfZrTi) 0.33 [ 14 ]. To validate the conclusion, we investigated the pressure evolutions of the crystal structure and the electronic structure for those M Te samples under high pressure. 2.2. Crystal structure Figures 3 a– 3 c show the pressure-dependent synchrotron X-ray diffraction (SXRD) patterns for the PbTe, AgPbBiTe 3 , and AgInSnPbBiTe 5 samples, respectively. For all the SXRD patterns, we performed the Rietveld refinement to confirm the structural type and to evaluate the lattice constant. See Tables S1–S3 and Figs. S4–S6 for details on refinements. On the basis of the refinement results, we established structural phase diagrams under high pressure (Figs. 3 d– 3 f) by plotting the pressure dependence of volume per unit formula ( Z ). For PbTe, the structural transition from NaCl-type to Pnma occurs at around 6.80 GPa, and the second transition to CsCl-type takes place at 14.28 GPa. The transition gradually occurred, hence the phase diagram contains mixed phases. The results on PbTe are consistent with the previous work by Li et al. [ 24 ]. For AgPbBiTe 3 and AgInSnPbBiTe 5 , similar phase diagrams were obtained, where the NaCl-type structure is stabilized up to ~ 10 GPa, and the Pnma phase is suppressed. The pressure where the CsCl-type phase is induced is common to the case of PbTe. In all the structural types including the CsCl-type phase, the lattice volume continuously decreases with pressure. Although the difference in the stability of the NaCl-type and Pnma structures may be related to the difference in lattice volume at ambient pressure, we consider that the Pnma phase is suppressed, and the NaCl-type phase is stabilized by the effect of alloying at the M site. We note that configurational entropy of mixing does not affect the structure of the CsCl-type phase, and lattice volume of the CsCl-type phase commonly decreases with pressure in three M Te sample. 2.3. Electronic structure To examine the effects of pressure and HEA states on the electronic structure, we performed X-ray absorption spectroscopy with partial fluorescence mode (PFY-XAS) for PbTe and AgInSnPbBiTe 5 . See Fig. S7 for pressure dependences of spectra, and analysis results on the Pb- L 3 and Bi- L 3 spectra. In general, the absorption spectra at the Pb- L 3 absorption edge are similar to those at the Bi- L 3 absorption edge. On the basis of analogically referring to other Pb- or Bi-containing compounds [ 30 , 31 ], we analyzed the spectra by assuming several peaks. An example of the fit for the PFY-XAS spectra at 27 GPa is shown in Fig. 4 a. The PFY-XAS spectra were fitted by assuming some Voigt functions with an arctan-like background [ 31 ]. In this study, we focus on the peaks of P1, P2, and P3, where peak P1 could be assigned as a dipole transition of the 2 p 3/2 electron into the 6 s state, and the peaks shown as P2 and P3 correspond to 6 d states of t 2g and e g , respectively [ 32 , 33 ]; we measure 2 p 3/2 → nd ( n > 6) transitions at the Pb L 3 absorption edge. There is a p density of states ( p DOS) above the Fermi level, however, we mainly observe the dipole-allowed transitions of Pb 2 p –6 s and Pb 2 p –6 d , and therefore, the observed spectra do not reflect the Pb 6 p DOS spectroscopically. The absorption spectra reflect the empty DOS above the Fermi level generally, with a core hole in the final state. For PbTe with a NaCl-type structure, there is a narrow band gap, and the p orbitals of Pb and Te near the Fermi energy are hybridized. See Figure S8 for the calculated DOS for PbTe [ 34 ]. The valence band is mainly composed of Te 5 p orbitals, and also contains the contribution from Pb 6 p and 6 s , while the conduction band is mainly composed of Pb 6 p orbitals, but also contains Te 5 p contributions. For PbTe with a CsCl-type structure, band gap is totally closed, and the DOS near the Fermi energy is explained by the contributions from Pb 6 p and 6 s orbitals, as well as the Te 5 p orbitals. Therefore, the pressure evolution of the 6s states which could be resolved in our high-resolution spectroscopy, may play an important role on the closing of the band gap as well as the emergence of superconductivity. The pressure dependences of the intensity and the energy of peak P1 in PbTe is shown in Fig. 4 b. The intensity of peak P1 in Fig. 4 b gradually increases with pressure, up to about 5 GPa. The increase in the intensity of P1 indicates an increase in the amount of holes in the Pb 6 s states, which indicates a modification of the band structure. In the middle-pressure phase, (between 5–15 GPa) the intensity of P1 does not show a significant change, while it increases remarkably in the HP phase ( P > 15 GPa). We note that PbTe with a NaCl-type or Pnma structure is a semiconductor with a band gap at the low-pressure regime, and we also note that the metallic phase is induced in a CsCl-type structure for pressures above 15 GPa [ 22 , 34 , 35 ]. The increase of the intensity of P1 corresponds with the increase of the unoccupied 6 s states of the Pb. This may correlate with the emergence of the superconductivity after the closing of the band gap at P > 15 GPa. On the other hand, the energy of peak P1 shifts to a lower incident energy until it reaches a pressure level of 5 GPa. The incident energy and the intensity do not change in the middle-pressure range of 5–17 GPa, and they start decreasing again for pressures above 18 GPa as shown in Fig. 4 b. The shift of the energy of peak P1 to a lower incident energy is explained by the upward shift of the Fermi level or change in the DOS at the Fermi level. Theory suggests that the energy shift of peak P1 may be influenced by the reduction of the band gap [ 35 ] and the theoretical band gap is in the same order as the energy shift of P1 at 5 GPa. The intensity of P3 (Pb 6 d DOS, e g ) shows a trend which is similar to the intensity of P1. The intensity of P2 (Pb 6 d DOS, t 2g ) on the other hand decreases with increasing pressure at P > 17 GPa (Fig. 4 c). It is interesting that there is a large change in the electronic structure for pressures above 20 GPa, but the crystal structure still retains its CsCl-type structure in this pressure range. In PbTe, superconductivity suddenly appears above 18 GPa, and T c decreases with pressure monotonically [ 22 ]. The present result possibly suggests that the change in the electronic structure is not favorable for the superconductivity of M Te, when it has transitioned to the CsCl-type structure. We also measured the PFY-XAS spectra at the Pb- L 3 absorption edges for AgInSnPbBiTe 5 as shown in Fig. S7. We observed similar trends in the pressure dependence of the electronic structures as those observed for PbTe. An example of the fit at 28.8 GPa is shown in Fig. 4 d. The analysis results on P1, P2, and P3 are plotted in Figs. 4 e and 4 f. Figure 4 e shows a gradual increase of the P1 intensity with pressure, which is similar to the case of PbTe. The trend of P2 is also similar for the entire pressure range, and that of P3 is basically similar between PbTe and AgInSnPbBiTe 5 . The PFY-XAS spectra at the Bi- L 3 absorption edge were also taken, and the analysis results are summarized in Fig. S7. In AgInSnPbBiTe 5 the pressure-induced change in the electronic structure seems to be common for Bi and Pb sites; the detailed results are shown under the Supporting Information section. In conclusion, the electronic structures of PbTe and AgInSnPbBiTe 5 show a similar pressure dependence, even though the structure of PbTe does not change much in the middle-pressure range ( Pnma + CsCl phase), which disappears in AgInSnPbBiTe 5 . Therefore, the difference in the robustness of superconductivity to pressure in the CsCl-type phase between PbTe and AgInSnPbBiTe 5 cannot be explained by the pressure evolutions of crystal and electronic structures. 3. Discussion From the structural viewpoint, the impact of the introduction of an HEA site is the suppression of the middle-pressure phase with a Pnma structure. In other words, the low-pressure phase with a NaCl-type structure is stabilized up to a higher pressure of P > 10 GPa in AgInSnPbBiTe 5 , whereas the NaCl-type phase disappears at ~ 5 GPa for PbTe. Interestingly, the trend of lattice constant in the CsCl-type structure under HP is quite similar for PbTe and AgInSnPbBiTe 5 . However, as revealed in Fig. 2 b, the pressure dependences of T c clearly differ since T c decreases with pressure for PbTe but does not change largely in the CsCl-type phase for AgInSnPbBiTe 5 . Furthermore, from the electronic-structure viewpoint, we cannot find a clear correlation between the robustness of superconductivity to pressure and the changes in electronic structure under high pressure. Although there is a possibility of the difference of the contribution of the 6 p states, which could not be measured in our spectra, to the conduction band to increase the number of the carriers in AgInSnPbBiTe 5 . The results show that the pressure phase diagram of the crystal structure is largely modified by the effect of Δ S mix . In contrast, the electronic structures are not sensitive to the effect of Δ S mix . To understand the HEA effects on structural and electronic properties for M Te under high pressure, further studies using various probes are needed. However, commonality on the robustness of superconductivity to external pressure in the superconducting HEA (TaNb) 0.67 (HfZrTi) 0.33 [ 14 ] and the HEA-type metal telluride AgInSnPbBiTe 5 would be demonstrating the universal characteristics of superconductivity in HEA-type materials. Thus, the present results propose that the combination of HP and HEA effects will open a new pathway to the development of new disordered superconductors with exotic superconducting states. 4. Conclusion We have studied the crystal and electronic structure and the robustness of superconducting states in a HEA-type metal telluride ( M Te; M = Ag, In, Sn, Pb, Bi) under high pressure using a polycrystalline sample, and the results were compared with the pressure effects for a middle-entropy system (AgPbBiTe 3 ) and a reference system of PbTe. PbTe exhibits a structural transition from a NaCl-type to an orthorhombic Pnma structure at low pressures, and further transitions to a CsCl-type structure at high pressures. When the superconductivity of the CsCl-type PbTe is observed, it is found that its superconducting transition temperature ( T c ) decreases with pressure. In contrast, in the HEA-type AgInSnPbBiTe 5 , T c is almost independent of pressure, for pressures ranging from 13.0 to 35.1 GPa. In addition, the middle-entropy system, AgPbBiTe 3 , shows a slight decrease in T c with pressure in the CsCl-type structure, which is intermediate trend between PbTe and AgInSnPbBiTe 5 . Those results suggest that the robustness of superconductivity to external pressure has been enhanced by the increase in configurational entropy of mixing at the metal ( M ) site in M Te. To further clarify the effects of the modification of the configurational entropy of mixing on the superconducting states and the electronic structure of M Te, synchrotron X-ray absorption spectroscopy with partial fluorescence mode (PFY-XAS) for three M Te polycrystalline samples of PbTe and AgInSnPbBiTe 5 were performed. Noticebly, the evolutions of electronic structure under high pressure do not largely differ between PbTe and AgInSnPbBiTe 5 ; hence, the difference in the robustness of superconductivity in PbTe and AgInSnPbBiTe 5 under high pressure is not explained by the difference in their electronic structure. According to the results of this work and previous work on a HEA (Ti-Zr-Hf-Nb-Ta), where the robustness of superconductivity was observed up to ~ 200 GPa, we propose that the robustness of superconductivity under high pressure would be a universal feature in HEA-type superconductors. Methods The polycrystalline sample of PbTe was synthesized by the solid-state reaction of Pb (99.9%) and Te (99.999%) at 900 ⁰C. To obtain a pellet for resistance measurements, pelletizing and second annealing were performed. The polycrystalline samples of AgPbBiTe 3 and AgInSnPbBiTe 5 were synthesized using an HP synthesis method where the pressure was kept below 3 GPa, and the temperature kept at 500 ⁰C for 30 minutes as described in Ref. 20. The precursor powders of AgPbBiTe 3 and AgInSnPbBiTe 5 were synthesized by a solid-state reaction of Ag powders (99.9%) and grains of In (99.99%), Sn (99.999%), Pb (99.9%), Bi (99.999%), and Te (99.999%) at 800 ⁰C, with the nominal compositions. The electrical resistance measurements were performed at ambient pressure using the conventional four-probe method on a GM refrigerator system. Resistance measurements under high pressure were performed on polycrystalline powder on a Physical Property Measurement System (Quantum Design) using an originally designed diamond anvil cell (DAC) with boron-doped diamond electrodes [ 36 – 38 ]. The sample was placed on the boron-doped diamond electrodes in the center of the bottom anvil. The surface of the bottom anvil, except for the sample space and electrical terminal, were covered with the undoped diamond insulating layer. The cubic boron nitride powders with ruby manometer were used as a pressure-transmitting medium. The applied pressure was estimated by the fluorescence from ruby powders [ 39 ] and the Raman spectrum from the culet of top diamond anvil [ 40 ] using an inVia Raman microscope (RENISHAW). The definition of T c is described in Fig. S1. Pressure dependences of the synchrotron X-ray powder diffraction (SXRD) patterns were measured at BL12B2, SPring-8, using a 3-pin plate diamond anvil cell (DAC, Almax easyLab Industries) with a CCD detection system at room temperature (~ 293 K). Culet size of the diamond anvil was 0.4 mm with a stainless-steel gasket. We took an arrangement of both incoming and outgoing x-ray beams passing through the diamonds with incident photon energy of 18 keV. A two-dimensional image of the CCD system was integrated using the FIT2D program [ 41 ]. Silicone oil was used as a pressure-transmitting medium, and pressure was monitored using the ruby fluorescence method. [ 42 ] The SXRD data was analyzed through Jana 2006 software [ 43 ] using the Rietveld method. The pressure dependence of the high-resolution X-ray absorption spectra was measured at beamline BL12XU, SPring-8. Membrane-controlled DACs with a 0.3 mm culet and that with a 0.4 mm culet were used for PbTe and AgInSnPbBiTe 5 , respectively, and silicone oil was used as a pressure-transmitting medium. Beryllium gaskets with a 3 mm diameter were pre-indented at the center. The thickness was approximately 67 µm for PbTe and 31 µm for AgInSnPbBiTe 5 , and the diameters of the sample chamber in the gaskets were approximately 110 µm for PbTe and 140 µm for AgInSnPbBiTe 5 . We employed X-ray absorption spectroscopy (XAS) with a partial fluorescence mode (PFY-XAS), which has an advantage of a higher resolution as compared to that of normal XAS [ 44 , 45 ]. We used the Be gasket in plane geometry where both incoming and outgoing x-ray beams passed through the Be gasket. A Johann-type spectrometer equipped with a spherically bent Si(555) analyzer crystal (radius of ~ 1 m), and a Si solid state detector were used to analyze the Bi L α 1 (10.839 keV, 3 d 5/2 -2 p 3/2 ) emission at the Bi L 3 absorption edge, and Pb L α 1 (10.551 eV, 3 d 5/2 -2 p 3/2 ) emission at the Pb L 3 absorption edge [ 46 ]. The incident beam is focused at 17 µm x 40 µm by the K-B mirror located at the sample position. Declarations Acknowledgements The measurements of the XRD patterns and the PFY-XAS spectra under pressure were performed BL12XU, and BL12B2, SPring-8 under SPring-8 Proposal Nos. 2020A4269, 2021A4253, & 2021B4254 (corresponding to Proposal Nos. 2019-2-261, 2021-1-009, 2021-1-404, & 2021-1-415 of NSRRC).The authors thank O. Miura for his supports in experiments. This work was partially supported by Grant-in-Aid for Scientific Research (KAKENHI) (Nos. 18KK0076, 21K18834, 21H00151) and Tokyo Metropolitan Government Advanced Research (H31-1). We thank Editage for English correction of the manuscript. Author contributions M.R.K., R.M., H.Y., Y.G. and Y.M. designed the research; M.R.K., A.Y., and Y.M. synthesized samples; R.M. and Y.T. performed resistance measurement; H.Y., H.I., and N.H. performed synchrotron experiments and analyzed the spectra of PFY-XAS; M.R.K., Y.N., A.Y., Y.G., and Y.M. analyzed the crystal structure; M.R.K., Y.N., H.Y., and Y.M. wrote the manuscript. 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High-Pressure Synthesis and Superconducting Properties of NaCl-Type In 1− x Pb x Te ( x = 0–0.8), Condens. Matter 5 , 14 (2020). Mitobe, T. et al. Superconductivity in In-doped AgSnBiTe 3 with possible band inversion, Rep. 11 , 22885 (2021). Swarbrick, J. C. et al. High Energy Resolution X-ray Absorption Spectroscopy of Environmentally Relevant Lead (II) Compounds, Chem. 48 , 10748 (2009). Yamaoka, H. et al. Electronic structures of Bi 2 Se 3 and Ag x Bi 2 Se 3 under pressure studied by high-resolution x-ray absorption spectroscopy and density functional theory calculations, Rev. B 102 , 155118 (2020). Rao K. J. & Wong, J. A XANES investigation of the bonding of divalent lead in solids, Chem. Phys. 81 , 4832 (1984). Retoux, R. et al. Valence state for bismuth in the superconducting bismuth cuprates, Rev. B 41 , 193 (1990). We obtained the electronic band structures of PbTe using CompES-X, NIMS database (https://compes-x.nims.go.jp/) Xu, L., Zheng, Y. & Zheng, J. C. Thermoelectric transport properties of PbTe under pressure, Rev. B 82 , 195102 (2010). Matsumoto, R. et al. Pressure-Induced Superconductivity in Sulfur-Doped SnSe Single Crystal Using Boron-Doped Diamond Electrode-Prefabricated Diamond Anvil Cell, Rev. Sci. Instrum. 87 , 076103 (2016). Matsumoto, R. et al. Diamond anvil cells using boron-doped diamond electrodes covered with undoped diamond insulating layer, Appl. Phys. Express 11 , 053101 (2018). Matsumoto, R. et al. Pressure-Induced Superconductivity in Sulfur-Doped SnSe Single Crystal Using Boron-Doped Diamond Electrode-Prefabricated Diamond Anvil Cell, J. Phys. Soc. Jpn. 87 , 124706 (2018). Irifune, T. et al. Ultrahard polycrystalline diamond from graphite, Nature 421 , 599 (2003). Piermarini, G. J. et al. Calibration of the pressure dependence of the R 1 ruby fluorescence line to 195 kbar, Appl. Phys. 46 , 2774 (1975). Hammersley, A. P. et al. Two-dimensional detector software: From real detector to idealised image or two-theta scan, High Press. Res. 14 , 235 (1996). Mao, H. K. & Bell, P. M.High-pressure physics, The 1-megabar mark on the ruby R 1 static pressure scale, Science 191 , 851 (1976). Petricek, V., Dusek, M.&Palatinus, L. Crystallographic Computing System JANA2006: General features, Z. Kristallogr. 229 , 345 (2014). Hämäläinen, K. et al. Elimination of the inner-shell lifetime broadening in x-ray-absorption spectroscopy, Phys. Rev. Lett. 67 , 2850 (1991). Hämäläinen, K. et al. Spin-dependent x-ray absorption of MnO and MnF 2 , Phys. Rev. B 46 , 14274 (1992). Yamaoka, H. Pressure dependence of the electronic structure of 4 f and 3 d electron systems studied by X-ray emission spectroscopy, High Press. Res. 36 , 262 (2016). Additional Declarations No competing interests reported. Supplementary Files SIKasemMTe20211209.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 08 Apr, 2022 Reviews received at journal 31 Mar, 2022 Reviewers agreed at journal 23 Mar, 2022 Reviewers invited by journal 23 Mar, 2022 Editor assigned by journal 22 Mar, 2022 Editor invited by journal 21 Feb, 2022 Submission checks completed at journal 21 Feb, 2022 First submitted to journal 01 Feb, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1319304","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":85389663,"identity":"cc85a3a5-ebb6-411a-a3a4-d1dc86197217","order_by":0,"name":"Yoshikazu Mizuguchi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYDACZjBpA+OyEa0lTYIELRBwWIKwGhjQbWd/Jvm17Xyd7owExg8/GPjyCGoxO8yQJi3bdlvC7EYCs2QPA1sxMVqOSUtCtDBIA/2S2EBYC2MbUMs5sC2/idTCzCb5se0ASAsbsbawMVsznEuW3HbmYZtljwExfjl//OHNH2V2/GbHkw/f+FFxjHCIgQAzD5hiBDrJ4FgCUVoYfyDYNcRpGQWjYBSMghEFAF0SNvscXCDJAAAAAElFTkSuQmCC","orcid":"","institution":"Tokyo Metropolitan University","correspondingAuthor":true,"prefix":"","firstName":"Yoshikazu","middleName":"","lastName":"Mizuguchi","suffix":""},{"id":85389664,"identity":"a5a40933-c5d8-46d5-8271-e70b04d83c99","order_by":1,"name":"Riad Kasem","email":"","orcid":"","institution":"Tokyo Metropolitan University","correspondingAuthor":false,"prefix":"","firstName":"Riad","middleName":"","lastName":"Kasem","suffix":""},{"id":85389665,"identity":"8b0eab1b-602a-4bd8-b9ab-827f6cd4d99c","order_by":2,"name":"Yuki Nakahira","email":"","orcid":"","institution":"Tokyo Metropolitan University","correspondingAuthor":false,"prefix":"","firstName":"Yuki","middleName":"","lastName":"Nakahira","suffix":""},{"id":85389666,"identity":"8470292d-c782-4cf0-b8dc-79e0e252a5c7","order_by":3,"name":"Hitoshi Yamaoka","email":"","orcid":"","institution":"RIKEN","correspondingAuthor":false,"prefix":"","firstName":"Hitoshi","middleName":"","lastName":"Yamaoka","suffix":""},{"id":85389667,"identity":"51827eeb-6a25-414d-ab67-74873576af9e","order_by":4,"name":"Ryo Matsumoto","email":"","orcid":"","institution":"National Institute for Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Ryo","middleName":"","lastName":"Matsumoto","suffix":""},{"id":85389668,"identity":"7d03115f-7063-44ba-ae92-4d639fe43ae7","order_by":5,"name":"Aichi Yamashita","email":"","orcid":"","institution":"Tokyo Metropolitan University","correspondingAuthor":false,"prefix":"","firstName":"Aichi","middleName":"","lastName":"Yamashita","suffix":""},{"id":85389669,"identity":"de9c9e2f-622e-4cdf-8b19-36ff1d9d04de","order_by":6,"name":"Hirofumi Ishii","email":"","orcid":"","institution":"National Synchrotron Radiation Research Center","correspondingAuthor":false,"prefix":"","firstName":"Hirofumi","middleName":"","lastName":"Ishii","suffix":""},{"id":85389670,"identity":"2a0677f4-a7eb-4da1-99c5-52276aee2d3a","order_by":7,"name":"Nozomu Hiraoka","email":"","orcid":"","institution":"National Synchrotron Radiation Research Center","correspondingAuthor":false,"prefix":"","firstName":"Nozomu","middleName":"","lastName":"Hiraoka","suffix":""},{"id":85389671,"identity":"5509e217-dca2-419d-85af-22dd24cd6489","order_by":8,"name":"Yoshihiko Takano","email":"","orcid":"","institution":"National Institute for Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Yoshihiko","middleName":"","lastName":"Takano","suffix":""},{"id":85389672,"identity":"9a48a016-3968-4e5b-a2b7-fd17dacfabeb","order_by":9,"name":"Yosuke Goto","email":"","orcid":"","institution":"Tokyo Metropolitan University","correspondingAuthor":false,"prefix":"","firstName":"Yosuke","middleName":"","lastName":"Goto","suffix":""}],"badges":[],"createdAt":"2022-02-02 01:29:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1319304/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1319304/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":18541465,"identity":"8c1be23f-70c2-404e-b80f-d63c7399e45a","added_by":"auto","created_at":"2022-02-23 20:20:26","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":111296,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSuperconducting transition in AgInSnPbBiTe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e5\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e under high pressure.a.\u003c/strong\u003e Temperature dependence of electrical resistance of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e measured using the conventional four-probe method. \u003cstrong\u003eb.\u003c/strong\u003eTemperature dependences of electrical resistance of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e measured using a diamond anvil cell (DAC).\u003c/p\u003e","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/deb6face982da59655d04d3d.png"},{"id":18541372,"identity":"5eb434e2-5df6-4031-af35-4c9cca22dfd6","added_by":"auto","created_at":"2022-02-23 20:17:26","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":133261,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePressure evolutions of \u003cem\u003eT\u003c/em\u003e\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e of metal tellurides with different configurational entropy of mixing. a.\u003c/strong\u003e Pressure dependence of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. Open and filled circles indicate the data taken without a pressure cell, and the data that was measured with DAC. The structural types are indicated according to structural analyses in Fig. 3d. \u003cstrong\u003eb.\u003c/strong\u003e Pressure dependences of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e for PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e.\u003cstrong\u003ec.\u003c/strong\u003e Schematic images of NaCl-type crystal structure and configurational entropy of mixing (D\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e) at the \u003cem\u003eM\u003c/em\u003e site of PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/aec4c5d5d8787452262d592c.png"},{"id":18541374,"identity":"a8ec5246-8927-41ca-858d-c2ad51925b96","added_by":"auto","created_at":"2022-02-23 20:17:26","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":176529,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePressure evolutions of crystal structure for metal tellurides with different configurational entropy of mixing.a–c.\u003c/strong\u003e SXRD patterns for PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. Note that the baseline height of the XRD pattern at each pressure scales to the pressure. \u003cstrong\u003ed–f.\u003c/strong\u003e Lattice volumes divided by \u003cem\u003eZ\u003c/em\u003e (chemical formula sum in a unit cell) for PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e are plotted as a function of pressure. In Fig. 3d, the analysis results reported in Ref. 24 (Li \u003cem\u003eet al.\u003c/em\u003e) are represented by orange lines. Structural types are shown in the figures.\u0026nbsp;\u003c/p\u003e","description":"","filename":"fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/0f9b52f0b223a9d872debf1d.png"},{"id":18541371,"identity":"9607ba92-22c7-440b-8cad-79f392a5ca6b","added_by":"auto","created_at":"2022-02-23 20:17:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":146786,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectronic structure of PbTe and AgInSnPbBiTe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e5\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e under high pressure. a.\u003c/strong\u003e Typical Pb-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e PFY-XAS spectrum and an example of the fit to the spectrum for PbTe at 27 GPa. \u003cstrong\u003eb.\u003c/strong\u003e Pressure dependence of the intensity and the energy of the peak P1 for PbTe. \u003cstrong\u003ec.\u003c/strong\u003e Pressure dependence of the intensity of the peaks P2 and P3 for PbTe. \u003cstrong\u003ed.\u003c/strong\u003e Typical Pb-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e PFY-XAS spectrum and an example of the fit to the spectrum for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e at 28.8 GPa. \u003cstrong\u003ee.\u003c/strong\u003e Pressure dependence of the intensity and the energy of the peak P1 for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. \u003cstrong\u003ef.\u003c/strong\u003e Pressure dependence of the intensity of the peaks P2 and P3 for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/e1465094cc26faa354df0457.png"},{"id":18541467,"identity":"15b675ff-3f29-427e-9aae-c2dc5983fa5f","added_by":"auto","created_at":"2022-02-23 20:20:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":731158,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/1f62b0c4-7818-4812-a03c-84ad6561ca4f.pdf"},{"id":18541466,"identity":"e219f378-73f2-4852-821c-a4be9c90d7a1","added_by":"auto","created_at":"2022-02-23 20:20:26","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":632139,"visible":true,"origin":"","legend":"","description":"","filename":"SIKasemMTe20211209.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1319304/v1/fed552cac448a8e36311a0e9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eRobustness of Superconductivity to External Pressure in High-Entropy-Alloy-Type Metal Telluride AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe superconductivity of disordered materials has been extensively studied because of an observation made on the insulator-superconductor transition or disorder-induced superconductivity [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In addition, recent studies on BiS\u003csub\u003e2\u003c/sub\u003e-based layered superconductors have shown the importance of controlling the local structural disorder to improve superconducting properties [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. As a new category of disordered superconductors, high-entropy alloys (HEAs), which are alloys containing five or more elements with an atomic concentration between 5% and 35% [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], have been extensively studied, leading to the discovery of a wide range of HEA superconductors [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. One of the notable features is the difference in characteristics of superconductivity among conventional metal or alloy superconductors, superconducting thin films, and HEA superconductors [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Furthermore, the robustness of superconductivity to extremely high pressure (HP), for pressures up to 190 GPa, in an HEA, (TaNb)\u003csub\u003e0.67\u003c/sub\u003e(HfZrTi)\u003csub\u003e0.33\u003c/sub\u003e, was observed [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The high configurational entropy of mixing (Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e) reduces the Gibbs\u0026rsquo;s free energy, and therefore stabilization of the phase is expected. The equation for calculating the Gibb\u0026rsquo;s free energy is Δ\u003cem\u003eG\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Δ\u003cem\u003eH\u003c/em\u003e - \u003cem\u003eT\u003c/em\u003eΔ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix,\u003c/sub\u003e where Δ\u003cem\u003eH\u003c/em\u003e is the enthalpy and \u003cem\u003eT\u003c/em\u003e is the absolute temperature. Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e can be calculated using the equation Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e = -\u003cem\u003eR\u003c/em\u003e \u0026sum;\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003eln\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, where, \u003cem\u003eR\u003c/em\u003e is the gas constant and \u003cem\u003ec\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e is the atomic ratio of the element (\u003cem\u003ei\u003c/em\u003e) [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The discovery of the robustness of superconductivity under an extremely high pressure was considered to be related to the high Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e, but similar robustness of superconductivity under an extremely high pressure and a high transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) of 19 K was observed in a low-entropy Nb-Ti alloy [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Therefore, the effects of Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e on the crystal structure, electronic structure, and superconducting properties of HEAs are still unclear. To address this issue, further investigation of HP effects on HEA-type materials is needed.\u003c/p\u003e \u003cp\u003eWe recently developed superconducting HEA-type compounds, in which one of the crystallographic sites is alloyed with the criterion similar to HEAs [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Since compounds with two or more crystallographic sites have unique chemical bonds, various (novel) effects of the introduction of HEA site to electronic and structural properties would be expected, which is so-called cocktail effect in the field of HEAs. In the layered BiS\u003csub\u003e2\u003c/sub\u003e-based superconductor \u003cem\u003eRE\u003c/em\u003e(O,F)BiS\u003csub\u003e2\u003c/sub\u003e, the rare-earth site (\u003cem\u003eRE\u003c/em\u003e) was alloyed with five different \u003cem\u003eRE\u003c/em\u003e elements [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], and the improvement of superconducting properties (bulk nature of superconductivity) with increasing Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e was observed [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e was not affected by Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e, and therefore its insensitivity to Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e in the BiS\u003csub\u003e2\u003c/sub\u003e-based superconductor is explained using a two-dimensional structure, since similar insensitivity was also observed in an \u003cem\u003eRE\u003c/em\u003e123 cuprate with an HEA-type \u003cem\u003eRE\u003c/em\u003e site [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In contrast, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e of NaCl-type metal telluride, which is the target phase of this study, shows that its sensitivity to Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e of HEA-type systems is larger than that of metal tellurides with one or two constituent elements at the metal site [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOn the basis of the facts described above, we considered that the metal telluride system is suitable for the discussion of the effects of high Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e on the crystal structure (phase stability) and superconducting properties under high pressure. Here, we studied the crystal structure, electronic structure, and superconducting properties of three tellurides (\u003cem\u003eM\u003c/em\u003eTe; \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Ag, In, Sn, Pb, Bi) with different Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e values at the \u003cem\u003eM\u003c/em\u003e site: PbTe (Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e = 0), AgPbBiTe\u003csub\u003e3\u003c/sub\u003e (Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e = 1.1\u003cem\u003eR\u003c/em\u003e), and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e (Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e = 1.6\u003cem\u003eR\u003c/em\u003e). The pressure evolutions of the crystal structure and electronic transport properties were reported in previous studies [\u003cspan additionalcitationids=\"CR23 CR24 CR25\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Although PbTe is a semiconductor under ambient and low pressures, it undergoes metallization under high pressures, and a superconducting transition is observed for pressures above 15 GPa [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. PbTe undergoes structural transitions as follows: cubic NaCl-type (\u003cem\u003eFm\u003c/em\u003e-3\u003cem\u003em\u003c/em\u003e) structure under low pressures, orthorhombic (\u003cem\u003ePnma\u003c/em\u003e) structure under moderate pressures, and cubic CsCl-type (\u003cem\u003ePm\u003c/em\u003e-3\u003cem\u003em\u003c/em\u003e) structure under HP [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. There is a report on synthesis and thermoelectric properties of AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, but the structural and physical properties of AgPbBiTe\u003csub\u003e3\u003c/sub\u003e have not been reported [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In this study, we established a phase diagram of the crystal structures, as well as one for superconductivity versus pressure for both AgPbBiTe\u003csub\u003e3\u003c/sub\u003e and AgSnInPbBiTe\u003csub\u003e5\u003c/sub\u003e. We also studied PbTe to examine the effects of configurational entropy of mixing. The pressure phase diagrams for the three tellurides are used to compare the crystal and electronic structures in detail. The results show that the pressure phase diagram of the crystal structure is largely modified by the effect of Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e. Furthermore, we found that the pressure dependence of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e in the HP phase (CsCl-type phase) exhibits a clear difference among the three compounds. In the HP phase, the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e for PbTe decreases with pressure, but that for HEA-type AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e exhibits a flat dependence, which suggests that the superconducting state of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e is robust to pressure. Our present findings show an analogical conclusion in the case of (TaNb)\u003csub\u003e0.67\u003c/sub\u003e(HfZrTi)\u003csub\u003e0.33\u003c/sub\u003e [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and suggest that the HEA effects universally enhance the robustness of superconductivity under high pressure.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Electrical resistance\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea shows the temperature dependence of the electrical resistance of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e measured using the conventional four-probe method at ambient pressure. \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ezero\u003c/sup\u003e was 1.8 K, which is slightly lower than that reported in previous research [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. We measured the electrical resistance (at National Institute for Materials Science) after several days since the sample was synthesized by HP annealing (at Tokyo Metropolitan University), and a slight aging effect of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e was noticed in \u003cem\u003eM\u003c/em\u003eTe superconductors synthesized under high pressure [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. We consider that the slight decrease in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e can be understood by the change in the internal strains because the XRD patterns do not show a remarkable change after aging in the HP-synthesized \u003cem\u003eM\u003c/em\u003eTe samples. Therefore, we continued to perform resistance measurements under high pressure using a diamond-anvil cell (DAC).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the temperature dependences of the electrical resistance of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e measured under various pressures with a DAC. Normal-state resistance decreases with pressure, for pressures up to 9.3 GPa and increases with pressure for pressures above 15.5 GPa. An onset of the superconducting transition was observed at 2 K under 6.5 GPa, and the zero-resistance state was observed at \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ezero\u003c/sup\u003e = 2 K under 10.2 GPa. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eonset\u003c/sup\u003e monotonously increased with pressure until it reached 13.0 GPa, and then it became insensitive to pressure for pressures ranging from 13.0 GPa to 35.1 GPa ( P\u0026thinsp;=\u0026thinsp;35.1 GPa is the chosen maximum pressure for the experiment). The results indicate that the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e in the CsCl-type structure of AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e is independent of applied pressure, while lattice constant decreases with pressure. The highest \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ezero\u003c/sup\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eonset\u003c/sup\u003e observed in the experiment on AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e are 4.5 K and 5.3 K, respectively. See Figure S1 for the determination criterion for \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eonset\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo compare the pressure evolution of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e in AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e with that of PbTe and AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, the pressure dependences of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eonset\u003c/sup\u003e for PbTe and AgPbBiTe\u003csub\u003e3\u003c/sub\u003e were examined (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec for structural difference and Figs. S2 and S3 for the resistance measurements), and the resulting \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e-\u003cem\u003eP\u003c/em\u003e plots are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. PbTe is a semiconductor at ambient and low pressures, but exhibits a pressure-induced superconducting transition above 17 GPa in the CsCl-type structure [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. At higher pressures, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e of PbTe monotonously decreases with pressure. In the case of AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, superconductivity was observed at \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;2.6 GPa, and at this instance \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eonset\u003c/sup\u003e reached 6.5 K. The \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e for AgPbBiTe\u003csub\u003e3\u003c/sub\u003e slightly decreases at high pressures. In AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, superconductivity is observed at low pressures as well because the low-pressure phase, having a NaCl-type structure, itself is a metal and shows superconductivity under ambient pressure (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). As demonstrated in the next section, the crystal-structure type under high pressure is CsCl-type for all the compounds. However, the trend of the pressure dependences of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e in the CsCl-type structure exhibit a clear difference among PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. The main findings of this study are that the robustness of superconductivity to pressure in HEA-type AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e is similar to that observed in (TaNb)\u003csub\u003e0.67\u003c/sub\u003e(HfZrTi)\u003csub\u003e0.33\u003c/sub\u003e [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. To validate the conclusion, we investigated the pressure evolutions of the crystal structure and the electronic structure for those \u003cem\u003eM\u003c/em\u003eTe samples under high pressure.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Crystal structure\u003c/h2\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea\u0026ndash;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec show the pressure-dependent synchrotron X-ray diffraction (SXRD) patterns for the PbTe, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e samples, respectively. For all the SXRD patterns, we performed the Rietveld refinement to confirm the structural type and to evaluate the lattice constant. See Tables S1\u0026ndash;S3 and Figs. S4\u0026ndash;S6 for details on refinements. On the basis of the refinement results, we established structural phase diagrams under high pressure (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed\u0026ndash;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef) by plotting the pressure dependence of volume per unit formula (\u003cem\u003eZ\u003c/em\u003e). For PbTe, the structural transition from NaCl-type to \u003cem\u003ePnma\u003c/em\u003e occurs at around 6.80 GPa, and the second transition to CsCl-type takes place at 14.28 GPa. The transition gradually occurred, hence the phase diagram contains mixed phases. The results on PbTe are consistent with the previous work by Li \u003cem\u003eet al.\u003c/em\u003e [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. For AgPbBiTe\u003csub\u003e3\u003c/sub\u003e and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, similar phase diagrams were obtained, where the NaCl-type structure is stabilized up to ~\u0026thinsp;10 GPa, and the \u003cem\u003ePnma\u003c/em\u003e phase is suppressed. The pressure where the CsCl-type phase is induced is common to the case of PbTe. In all the structural types including the CsCl-type phase, the lattice volume continuously decreases with pressure. Although the difference in the stability of the NaCl-type and \u003cem\u003ePnma\u003c/em\u003e structures may be related to the difference in lattice volume at ambient pressure, we consider that the \u003cem\u003ePnma\u003c/em\u003e phase is suppressed, and the NaCl-type phase is stabilized by the effect of alloying at the \u003cem\u003eM\u003c/em\u003e site. We note that configurational entropy of mixing does not affect the structure of the CsCl-type phase, and lattice volume of the CsCl-type phase commonly decreases with pressure in three \u003cem\u003eM\u003c/em\u003eTe sample.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Electronic structure\u003c/h2\u003e \u003cp\u003eTo examine the effects of pressure and HEA states on the electronic structure, we performed X-ray absorption spectroscopy with partial fluorescence mode (PFY-XAS) for PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. See Fig. S7 for pressure dependences of spectra, and analysis results on the Pb-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e and Bi-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e spectra. In general, the absorption spectra at the Pb-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edge are similar to those at the Bi-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edge. On the basis of analogically referring to other Pb- or Bi-containing compounds [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], we analyzed the spectra by assuming several peaks. An example of the fit for the PFY-XAS spectra at 27 GPa is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. The PFY-XAS spectra were fitted by assuming some Voigt functions with an arctan-like background [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In this study, we focus on the peaks of P1, P2, and P3, where peak P1 could be assigned as a dipole transition of the 2\u003cem\u003ep\u003c/em\u003e\u003csub\u003e3/2\u003c/sub\u003e electron into the 6\u003cem\u003es\u003c/em\u003e state, and the peaks shown as P2 and P3 correspond to 6\u003cem\u003ed\u003c/em\u003e states of \u003cem\u003et\u003c/em\u003e\u003csub\u003e2g\u003c/sub\u003e and \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e, respectively [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]; we measure 2\u003cem\u003ep\u003c/em\u003e\u003csub\u003e3/2\u003c/sub\u003e \u0026rarr; \u003cem\u003end\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;6) transitions at the Pb \u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edge. There is a \u003cem\u003ep\u003c/em\u003e density of states (\u003cem\u003ep\u003c/em\u003e DOS) above the Fermi level, however, we mainly observe the dipole-allowed transitions of Pb 2\u003cem\u003ep\u003c/em\u003e\u0026ndash;6\u003cem\u003es\u003c/em\u003e and Pb 2\u003cem\u003ep\u003c/em\u003e\u0026ndash;6\u003cem\u003ed\u003c/em\u003e, and therefore, the observed spectra do not reflect the Pb 6\u003cem\u003ep\u003c/em\u003e DOS spectroscopically. The absorption spectra reflect the empty DOS above the Fermi level generally, with a core hole in the final state.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor PbTe with a NaCl-type structure, there is a narrow band gap, and the \u003cem\u003ep\u003c/em\u003e orbitals of Pb and Te near the Fermi energy are hybridized. See Figure S8 for the calculated DOS for PbTe [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The valence band is mainly composed of Te 5\u003cem\u003ep\u003c/em\u003e orbitals, and also contains the contribution from Pb 6\u003cem\u003ep\u003c/em\u003e and 6\u003cem\u003es\u003c/em\u003e, while the conduction band is mainly composed of Pb 6\u003cem\u003ep\u003c/em\u003e orbitals, but also contains Te 5\u003cem\u003ep\u003c/em\u003e contributions. For PbTe with a CsCl-type structure, band gap is totally closed, and the DOS near the Fermi energy is explained by the contributions from Pb 6\u003cem\u003ep\u003c/em\u003e and 6\u003cem\u003es\u003c/em\u003e orbitals, as well as the Te 5\u003cem\u003ep\u003c/em\u003e orbitals. Therefore, the pressure evolution of the 6s states which could be resolved in our high-resolution spectroscopy, may play an important role on the closing of the band gap as well as the emergence of superconductivity.\u003c/p\u003e \u003cp\u003eThe pressure dependences of the intensity and the energy of peak P1 in PbTe is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. The intensity of peak P1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb gradually increases with pressure, up to about 5 GPa. The increase in the intensity of P1 indicates an increase in the amount of holes in the Pb 6\u003cem\u003es\u003c/em\u003e states, which indicates a modification of the band structure. In the middle-pressure phase, (between 5\u0026ndash;15 GPa) the intensity of P1 does not show a significant change, while it increases remarkably in the HP phase (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;15 GPa). We note that PbTe with a NaCl-type or \u003cem\u003ePnma\u003c/em\u003e structure is a semiconductor with a band gap at the low-pressure regime, and we also note that the metallic phase is induced in a CsCl-type structure for pressures above 15 GPa [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The increase of the intensity of P1 corresponds with the increase of the unoccupied 6\u003cem\u003es\u003c/em\u003e states of the Pb. This may correlate with the emergence of the superconductivity after the closing of the band gap at \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;15 GPa.\u003c/p\u003e \u003cp\u003eOn the other hand, the energy of peak P1 shifts to a lower incident energy until it reaches a pressure level of 5 GPa. The incident energy and the intensity do not change in the middle-pressure range of 5\u0026ndash;17 GPa, and they start decreasing again for pressures above 18 GPa as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. The shift of the energy of peak P1 to a lower incident energy is explained by the upward shift of the Fermi level or change in the DOS at the Fermi level. Theory suggests that the energy shift of peak P1 may be influenced by the reduction of the band gap [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] and the theoretical band gap is in the same order as the energy shift of P1 at 5 GPa.\u003c/p\u003e \u003cp\u003eThe intensity of P3 (Pb 6\u003cem\u003ed\u003c/em\u003e DOS, \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e) shows a trend which is similar to the intensity of P1. The intensity of P2 (Pb 6\u003cem\u003ed\u003c/em\u003e DOS, \u003cem\u003et\u003c/em\u003e\u003csub\u003e2g\u003c/sub\u003e) on the other hand decreases with increasing pressure at \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;17 GPa (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). It is interesting that there is a large change in the electronic structure for pressures above 20 GPa, but the crystal structure still retains its CsCl-type structure in this pressure range. In PbTe, superconductivity suddenly appears above 18 GPa, and \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e decreases with pressure monotonically [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The present result possibly suggests that the change in the electronic structure is not favorable for the superconductivity of \u003cem\u003eM\u003c/em\u003eTe, when it has transitioned to the CsCl-type structure.\u003c/p\u003e \u003cp\u003eWe also measured the PFY-XAS spectra at the Pb-\u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edges for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e as shown in Fig. S7. We observed similar trends in the pressure dependence of the electronic structures as those observed for PbTe. An example of the fit at 28.8 GPa is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed. The analysis results on P1, P2, and P3 are plotted in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee shows a gradual increase of the P1 intensity with pressure, which is similar to the case of PbTe. The trend of P2 is also similar for the entire pressure range, and that of P3 is basically similar between PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. The PFY-XAS spectra at the Bi-\u003cem\u003eL\u003c/em\u003e3 absorption edge were also taken, and the analysis results are summarized in Fig. S7. In AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e the pressure-induced change in the electronic structure seems to be common for Bi and Pb sites; the detailed results are shown under the Supporting Information section. In conclusion, the electronic structures of PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e show a similar pressure dependence, even though the structure of PbTe does not change much in the middle-pressure range (\u003cem\u003ePnma\u003c/em\u003e\u0026thinsp;+\u0026thinsp;CsCl phase), which disappears in AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. Therefore, the difference in the robustness of superconductivity to pressure in the CsCl-type phase between PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e cannot be explained by the pressure evolutions of crystal and electronic structures.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eFrom the structural viewpoint, the impact of the introduction of an HEA site is the suppression of the middle-pressure phase with a \u003cem\u003ePnma\u003c/em\u003e structure. In other words, the low-pressure phase with a NaCl-type structure is stabilized up to a higher pressure of \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;10 GPa in AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, whereas the NaCl-type phase disappears at ~\u0026thinsp;5 GPa for PbTe. Interestingly, the trend of lattice constant in the CsCl-type structure under HP is quite similar for PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. However, as revealed in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, the pressure dependences of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e clearly differ since \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e decreases with pressure for PbTe but does not change largely in the CsCl-type phase for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. Furthermore, from the electronic-structure viewpoint, we cannot find a clear correlation between the robustness of superconductivity to pressure and the changes in electronic structure under high pressure. Although there is a possibility of the difference of the contribution of the 6\u003cem\u003ep\u003c/em\u003e states, which could not be measured in our spectra, to the conduction band to increase the number of the carriers in AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eThe results show that the pressure phase diagram of the crystal structure is largely modified by the effect of Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e. In contrast, the electronic structures are not sensitive to the effect of Δ\u003cem\u003eS\u003c/em\u003e\u003csub\u003emix\u003c/sub\u003e. To understand the HEA effects on structural and electronic properties for \u003cem\u003eM\u003c/em\u003eTe under high pressure, further studies using various probes are needed. However, commonality on the robustness of superconductivity to external pressure in the superconducting HEA (TaNb)\u003csub\u003e0.67\u003c/sub\u003e(HfZrTi)\u003csub\u003e0.33\u003c/sub\u003e [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and the HEA-type metal telluride AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e would be demonstrating the universal characteristics of superconductivity in HEA-type materials. Thus, the present results propose that the combination of HP and HEA effects will open a new pathway to the development of new disordered superconductors with exotic superconducting states.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eWe have studied the crystal and electronic structure and the robustness of superconducting states in a HEA-type metal telluride (\u003cem\u003eM\u003c/em\u003eTe; \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Ag, In, Sn, Pb, Bi) under high pressure using a polycrystalline sample, and the results were compared with the pressure effects for a middle-entropy system (AgPbBiTe\u003csub\u003e3\u003c/sub\u003e) and a reference system of PbTe. PbTe exhibits a structural transition from a NaCl-type to an orthorhombic \u003cem\u003ePnma\u003c/em\u003e structure at low pressures, and further transitions to a CsCl-type structure at high pressures. When the superconductivity of the CsCl-type PbTe is observed, it is found that its superconducting transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) decreases with pressure. In contrast, in the HEA-type AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is almost independent of pressure, for pressures ranging from 13.0 to 35.1 GPa. In addition, the middle-entropy system, AgPbBiTe\u003csub\u003e3\u003c/sub\u003e, shows a slight decrease in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e with pressure in the CsCl-type structure, which is intermediate trend between PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. Those results suggest that the robustness of superconductivity to external pressure has been enhanced by the increase in configurational entropy of mixing at the metal (\u003cem\u003eM\u003c/em\u003e) site in \u003cem\u003eM\u003c/em\u003eTe. To further clarify the effects of the modification of the configurational entropy of mixing on the superconducting states and the electronic structure of \u003cem\u003eM\u003c/em\u003eTe, synchrotron X-ray absorption spectroscopy with partial fluorescence mode (PFY-XAS) for three \u003cem\u003eM\u003c/em\u003eTe polycrystalline samples of PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e were performed. Noticebly, the evolutions of electronic structure under high pressure do not largely differ between PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e; hence, the difference in the robustness of superconductivity in PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e under high pressure is not explained by the difference in their electronic structure. According to the results of this work and previous work on a HEA (Ti-Zr-Hf-Nb-Ta), where the robustness of superconductivity was observed up to ~\u0026thinsp;200 GPa, we propose that the robustness of superconductivity under high pressure would be a universal feature in HEA-type superconductors.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe polycrystalline sample of PbTe was synthesized by the solid-state reaction of Pb (99.9%) and Te (99.999%) at 900 ⁰C. To obtain a pellet for resistance measurements, pelletizing and second annealing were performed. The polycrystalline samples of AgPbBiTe\u003csub\u003e3\u003c/sub\u003e and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e were synthesized using an HP synthesis method where the pressure was kept below 3 GPa, and the temperature kept at 500 ⁰C for 30 minutes as described in Ref. 20. The precursor powders of AgPbBiTe\u003csub\u003e3\u003c/sub\u003e and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e were synthesized by a solid-state reaction of Ag powders (99.9%) and grains of In (99.99%), Sn (99.999%), Pb (99.9%), Bi (99.999%), and Te (99.999%) at 800 ⁰C, with the nominal compositions.\u003c/p\u003e \u003cp\u003eThe electrical resistance measurements were performed at ambient pressure using the conventional four-probe method on a GM refrigerator system. Resistance measurements under high pressure were performed on polycrystalline powder on a Physical Property Measurement System (Quantum Design) using an originally designed diamond anvil cell (DAC) with boron-doped diamond electrodes [\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The sample was placed on the boron-doped diamond electrodes in the center of the bottom anvil. The surface of the bottom anvil, except for the sample space and electrical terminal, were covered with the undoped diamond insulating layer. The cubic boron nitride powders with ruby manometer were used as a pressure-transmitting medium. The applied pressure was estimated by the fluorescence from ruby powders [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] and the Raman spectrum from the culet of top diamond anvil [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] using an inVia Raman microscope (RENISHAW). The definition of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is described in Fig. S1.\u003c/p\u003e \u003cp\u003ePressure dependences of the synchrotron X-ray powder diffraction (SXRD) patterns were measured at BL12B2, SPring-8, using a 3-pin plate diamond anvil cell (DAC, Almax easyLab Industries) with a CCD detection system at room temperature (~\u0026thinsp;293 K). Culet size of the diamond anvil was 0.4 mm with a stainless-steel gasket. We took an arrangement of both incoming and outgoing x-ray beams passing through the diamonds with incident photon energy of 18 keV. A two-dimensional image of the CCD system was integrated using the FIT2D program [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Silicone oil was used as a pressure-transmitting medium, and pressure was monitored using the ruby fluorescence method. [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] The SXRD data was analyzed through Jana 2006 software [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e] using the Rietveld method.\u003c/p\u003e \u003cp\u003eThe pressure dependence of the high-resolution X-ray absorption spectra was measured at beamline BL12XU, SPring-8. Membrane-controlled DACs with a 0.3 mm culet and that with a 0.4 mm culet were used for PbTe and AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, respectively, and silicone oil was used as a pressure-transmitting medium. Beryllium gaskets with a 3 mm diameter were pre-indented at the center. The thickness was approximately 67 \u0026micro;m for PbTe and 31 \u0026micro;m for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e, and the diameters of the sample chamber in the gaskets were approximately 110 \u0026micro;m for PbTe and 140 \u0026micro;m for AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e. We employed X-ray absorption spectroscopy (XAS) with a partial fluorescence mode (PFY-XAS), which has an advantage of a higher resolution as compared to that of normal XAS [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. We used the Be gasket in plane geometry where both incoming and outgoing x-ray beams passed through the Be gasket. A Johann-type spectrometer equipped with a spherically bent Si(555) analyzer crystal (radius of ~\u0026thinsp;1 m), and a Si solid state detector were used to analyze the Bi \u003cem\u003eL\u003c/em\u003eα\u003csub\u003e1\u003c/sub\u003e (10.839 keV, 3\u003cem\u003ed\u003c/em\u003e\u003csub\u003e5/2\u003c/sub\u003e-2\u003cem\u003ep\u003c/em\u003e\u003csub\u003e3/2\u003c/sub\u003e) emission at the Bi \u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edge, and Pb \u003cem\u003eL\u003c/em\u003eα\u003csub\u003e1\u003c/sub\u003e (10.551 eV, 3\u003cem\u003ed\u003c/em\u003e\u003csub\u003e5/2\u003c/sub\u003e-2\u003cem\u003ep\u003c/em\u003e\u003csub\u003e3/2\u003c/sub\u003e) emission at the Pb \u003cem\u003eL\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e absorption edge [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The incident beam is focused at 17 \u0026micro;m x 40 \u0026micro;m by the K-B mirror located at the sample position.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe measurements of the XRD patterns and the PFY-XAS spectra under pressure were performed BL12XU, and BL12B2, SPring-8 under SPring-8 Proposal Nos. 2020A4269, 2021A4253, \u0026amp; 2021B4254 (corresponding to Proposal Nos. 2019-2-261, 2021-1-009, 2021-1-404, \u0026amp; 2021-1-415 of NSRRC).The authors thank O. Miura for his supports in experiments. This work was partially supported by Grant-in-Aid for Scientific Research (KAKENHI) (Nos. 18KK0076, 21K18834, 21H00151) and Tokyo Metropolitan Government Advanced Research (H31-1). We thank Editage for English correction of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM.R.K., R.M., H.Y., Y.G. and Y.M. designed the research; M.R.K., A.Y., and Y.M. synthesized samples; R.M. and Y.T. performed resistance measurement; H.Y., H.I., and N.H. performed synchrotron experiments and analyzed the spectra of PFY-XAS; M.R.K., Y.N., A.Y., Y.G., and Y.M. analyzed the crystal structure; M.R.K., Y.N., H.Y., and Y.M. wrote the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Authors declare no Competing Financial or Non-Financial Interests\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author (Y.M.) upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDubi, Y., Meir, Y. \u0026amp; Y. 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Res. \u003cstrong\u003e36\u003c/strong\u003e, 262 (2016).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-1319304/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1319304/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigh-entropy-alloy (HEA) superconductors are a new class of disordered superconductors. However, commonality of superconducting characteristics of HEA materials is unclear. Here, we have investigated the crystal and electronic structure, and the robustness of superconducting states in a HEA-type metal telluride (\u003cem\u003eM\u003c/em\u003eTe; \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Ag, In, Sn, Pb, Bi) under high pressure, and the results were compared with the pressure effects for a middle-entropy system (AgPbBiTe\u003csub\u003e3\u003c/sub\u003e) and a reference system of PbTe. When the crystal structure is CsCl-type, all phases show superconductivity under high pressure but exhibit different pressure dependences of the transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e). For PbTe, its \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e decreases with pressure. In contrast, the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e of HEA-type AgInSnPbBiTe\u003csub\u003e5\u003c/sub\u003e is almost independent of pressure, for pressures ranging from 13.0 to 35.1 GPa. Those results suggest that the robustness of superconductivity to external pressure is linked to the configurational entropy of mixing at the \u003cem\u003eM\u003c/em\u003e site in \u003cem\u003eM\u003c/em\u003eTe. Since the trend is quite similar to previous work on a HEA (Ti-Zr-Hf-Nb-Ta), where the robustness of superconductivity was observed up to ~\u0026thinsp;200 GPa, we propose that the robustness of superconductivity under high pressure would be a universal feature in HEA-type superconductors.\u003c/p\u003e","manuscriptTitle":"Robustness of Superconductivity to External Pressure in High-Entropy-Alloy-Type Metal Telluride AgInSnPbBiTe5","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-02-23 20:17:24","doi":"10.21203/rs.3.rs-1319304/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2022-04-08T17:49:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-04-01T02:14:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"69aa0244-f32e-45c0-9325-852db9a26421","date":"2022-03-24T00:53:01+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-03-23T17:04:46+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-03-22T14:52:19+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2022-02-21T11:10:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-02-21T11:02:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2022-02-02T01:17:14+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2c5fe3ae-015d-422c-8d78-585331f49c56","owner":[],"postedDate":"February 23rd, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2022-04-26T07:14:26+00:00","versionOfRecord":[],"versionCreatedAt":"2022-02-23 20:17:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1319304","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1319304","identity":"rs-1319304","version":["v1"]},"buildId":"J0_U0BvcaRcwD8yVFaRlm","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}