List of HEA superconductors and HEA-type superconducting compounds; composition, mixing entropy, Tc, and structural type are summarized.
Since the discovery of superconductivity in a high-entropy alloy (HEA) Ti-Zr-Nb-Hf-Ta in 2014, the community of superconductor science has explored new HEA superconductors to find the merit of the HEA states on superconducting properties. Since 2018, we have developed “HEA-type” compounds as superconductors or thermoelectric materials. As well known, compounds like intermetallic compounds or layered compounds are composed of multi crystallographic sites. In a HEA-type compounds, one or more sites are alloyed and total mixing entropy satisfies with the criterion of HEA. Herein, we summarize the synthesis methods, the crystal structural variation and superconducting properties of the HEA-type compounds, which include NaCl-type metal tellurides, CuAl2-type transition metal zirconides, high-Tc cuprates, and BiS2-based layered superconductors. The effects of the introduction of a HEA site in various kinds of complicated compounds are discussed from the structural-dimensionality viewpoint.
- layered compounds
- material design
- high entropy alloy
1.1 Superconducting materials
Superconductivity is a quantum phenomenon, which is characterized by zero-resistivity states in electrical resistivity and exclusion of magnetic flux from a superconductor [1, 2]. Superconductivity has provided many exotic research topics not only in the field of science but also in application of superconductors. The zero-resistivity states can achieve large-scale electricity transport with ultra-low energy loss, very high magnetic fields, which has been used in various devices like a magnetic resonance imaging (MRI) and a superconducting Maglev train. Although superconductor devises look perfect, the use of superconductors are regulated by temperature in reality because superconducting states are observed only at temperatures below a superconducting transition temperature (Tc), which is a parameter unique to the superconductor. To use superconducting devices, the system must be cooled down to low temperatures lower than the Tc of its superconducting components. Therefore, discovery of high-Tc superconductors has been desired.
In 1986, superconductivity with a high Tc in a Cu oxide (La,Ba)2CuO4 was discovered [3, 4]. Soon after the discovery, Tc of the Cu-oxide superconductor (cuprate) family reached 90 K for REBa2Cu3O7-d (RE: rare earth) , which is higher than liquid nitrogen temperature, and finally reached 135 K in a Hg-Ba-Ca-Gu-O system . After the discovery of the cuprate family, many layered compounds have been searched for high-Tc superconductivity. In 2001, superconductivity in MgB2 with a Tc of 39 K was reported . Furthermore, in 2008, FeAs-based layered superconductors REFeAsO1-xFx with a Tc exceeding 50 K were discovered [8, 9]. Particularly, in the cuprates and FeAs-based families, unconventional (non-phonon-mediated) mechanisms of superconductivity has been proposed to explain their high Tc .
A surprising discovery of superconductivity at very high Tc of 203 K in H3S was reported in 2015 . The phenomenon could be achieved at extremely high pressures above 150 GPa, the high Tc and possible conventional (phonon-mediated) mechanisms have recently been attracting many researchers in the field of condensed matter physics. Furthermore, higher Tcs have been reported in related hydrides, LaH10 (Tc > 250 K at ~200 GPa) [12, 13] and a carbonaceous sulfur hydride system (Tc = 287.7 K at 267 GPa) . To use high-Tc superconducting states in hydrides, discovery of new superconducting hydrides which become superconductive at ambient pressure. The possible strategy to realize that is the utilization of chemical pressure effects, which are applied via chemical substitutions and sometimes work like external pressure effects. Therefore, further investigations on chemical pressure effects in novel superconductors are needed, and high-entropy alloying of compounds would be one of the routs to chemically modify the crystal structure of superconductors.
1.2 Superconductivity in high-entropy alloys
Although layered compounds had been the central topic in searching high-Tc and/or unconventional superconductors over the last three decades, recent works on new superconductors have focused on various kinds of materials, which includes complicated compounds and pure metals as well. Among them, high-entropy-alloy (HEA) superconductors have been a developing field of study .
HEA is an alloy possessing high configurational mixing entropy (ΔSmix), which is achieved by making the alloy with more than five constituent elements with an occupancy ranging 5 to 35 at% for each element [16, 17]. Typically, ΔSmix of HEA is calculated by ΔSmix = −R Σi ci ln ci, where ci and R are the compositional ratio and the gas constant , and reaches 1.5R. Due to high ΔSmix, HEAs exhibit stability or high performance in high temperature and/or extreme conditions . Therefore, HEAs have been extensively studied in the fields of materials science and engineering.
In 2014, Koželj et al. reported superconductivity with Tc = 7.3 K in a HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 . The HEA superconductor has a bcc structure with a space group of Im-3 m. In Figure 1, we compare the crystal structures of (a) a pure Nb metal (Tc = 9.2 K), (b) a NbTi alloy (Tc ~ 10 K), which is the mostly-used practical superconductor, and (c) HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. All those materials show superconductivity and the crystal structure type is the same. The difference between them is the mixing entropy ΔSmix and Tc. Although the Tc of HEA is lower than that of the other two, it was surprising for researchers that such a disordered alloy exhibits superconductivity with bulk nature. After the discovery of Ref. , various HEA superconductors have been developed; material information [18, 19, 20, 21, 22, 23, 24, 25, 26] is listed in Table 1.
|(HfTaWIr)0.6Re0.4||1.50||1.9||bcc + hcp|
|(HfTaWIr)0.5Re0.5||1.39||2.7||bcc + hcp|
|(HfTaWPt)0.5Re0.5||1.39||2.2||bcc + hcp|
As shown in Figure 2, a superconducting transition was observed in Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 . The temperature dependence of electrical resistivity (Figure 2(a)) shows metallic behavior but exhibits a relatively small residual resistivity ratio (RRR) at low temperatures. This would be due to the presence of disorder, and a similar trend has been observed in various HEA-type superconductors. Bulk superconductivity could be confirmed through specific heat measurement as shown in Figure 2(b). From specific heat data, it has been found that most HEA superconductors exhibit conventional (phonon-mediated) pairing states.
Tc of HEA superconductors show correlation with valence electron count (VEC) [15, 21, 27]. The type-A HEAs with lower VEC exhibit a dependence of Tc on VEC similar to that for crystalline metals, alloys, and amorphous materials, and the Tc of HEAs are intermediate between crystalline materials and amorphous. In contrast, the Tc of the type-C HEAs with middle VEC shows opposite behavior to that for other forms. For the type-B HEAs, the trend of Tc on VEC seems resembling that for other forms, but their Tcs are clearly lower than that for crystalline and amorphous materials. As mentioned in Ref. , there would be a clear effect of crystallinity on Tc at the same VEC range, but the origin of the different trends between type-A, type-B, and type-C regimes have not been clarified from physical viewpoint (Figure 3).
Another notable character of HEA is a robustness of superconductivity to extremely high pressure. As reported in Ref. , the Tc of Ta-Nb-Hf-Zr-Ti slightly increases by external pressure effect and the 10 K-class Tc maintains under extreme pressures like 200 GPa. However, the robustness of superconductivity to extremely high pressure was reported for simpler NbTi with a clear increase in Tc to 19.1 K at 261 GPa . Therefore, the issue if HEA can improve the stability of superconductor under extremely high pressures has not been clarified.
1.3 Concept of HEA-type compounds
As described in subsection 1–2, superconductivity in HEAs has been discovered and been regarded as a new research field of superconductivity. However, the merit of HEA states for superconductors has not been fully understood. Therefore, development of new types of HEA superconductors is needed. The hint to expand the material variation of HEA superconductors was proposed in Ref. , in which a HEA superconductor with a CsCl-type structure was reported. Since the CsCl structure contains two independent crystallographic sites, we have flexibility of elemental solution at the two sites. When calculating total ΔSmix of (ScZrNbTa)0.65(RhPd)0.35 by taking the sum of ΔSmixs for site-1 and site-2, it appears to reach very high ΔSmix of 1.79R. A similar site separation has been observed in (Nb0.11Re0.56)(HfZrTi)0.33 . Motivated by those studies on HEAs with site separation, we have tried to synthesize various “HEA-type compounds”, which contain NaCl-type metal chalcogenides [31, 32, 33], CuAl2-type tetragonal TrZr2 (Tr: Fe, Co, Ni, Cu, Rh, Ir) [34, 35], high-Tc RE123 cuprates , and BiS2-based layered superconductors [37, 38]. The concept of HEA-type compounds it that we achieve a high ΔSmix by site-selective alloying. As shown in Figure 4, HEA-type compounds have a HEA-type site, in which five or more elements are solving and a normal site, which is not in the HEA state. The list of superconducting HEA-type compounds is shown in Table 2. By studying HEA effects to crystal structure and physical properties in various crystal structures, we could identify the merit of HEA states in those compounds. In section 2, we review the material synthesis, crystal structure, and physical properties of newly synthesized HEA-type compounds.
2. NaCl-type metal chalcogenides MCh
2.1 Metal tellurides MTe
The NaCl-type metal telluride family is one of the hot systems because it includes thermoelectric PbTe  and a topological crystalline insulator SnTe . For superconducting tellurides, high-pressure synthesis was used to stabilize the NaCl-type structure [42, 43, 44]. For example, the low-pressure phase of InTe has a TlSe-type structure, but the high-pressure phase of InTe has a NaCl-type structure. The high-pressure phase can be obtained by high-pressure synthesis [43, 44]. Motivated by these facts, we tried to synthesize HEA-type tellurides MTe where the M site is in the HEA state (see Figure 4(b) for crystal structure) by high-pressure synthesis.
Figure 5(a) shows the temperature dependence of electrical resistivity for AgInSnPbBiTe5, in which the M site is evenly occupied by Ag, In, Sn, Pb, and Bi (five metals) . Very small RRR was observed, which is a similar trend to that in HEA superconductors . In addition, four different MTe (M: Ag, In, Cd, Sn, Sb, Pb, Bi) superconductors with a HEA-type site has been obtained . Interestingly, there is a correlation between the lattice constant and Tc in HEA-type MTe. In Figure 5(b), the data for typical MTe superconductors are plotted. It is found that the trend that Tc increases with increasing lattice constant is common among the plotted MTe. The Tcs of HEA-type are, however, lower than those of low-entropy tellurides, such as InTe and (In,Sn)Te. Therefore, the introduction of the HEA-type M site is found to negatively work for Tc in MTe. This negative effect would be due to the direct effect of strong disorder to the M-Te bonding states and hence electronic states.
2.2 Hybrid high-entropy alloying in MCh
The Te site of MTe can be substituted by S and Se. The flexibility of both M and Te sites to element substitution enables us to design “hybrid HEA”, in which both sites are alloyed . Figure 6(a) shows the X-ray diffraction patterns for (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex. Notably, mixing many elements at two sites does not result in phase separation, and a single-phase sample was obtained for x = 0.25, while small impurity phases were detected for x = 0.5. For x = 0.25, as displayed in Figure 6(b), the ΔSmix for the M and Ch sites are 1.38R and 0.51R, and the total ΔSmix reaches 1.89R. Furthermore, the total ΔSmix for x = 0.5 reaches 2.00R. These ΔSmix values are clearly higher than that for HEAs (Table 1). Therefore, alloying at two or more sites (hybrid high-entropy alloying) results in very high total ΔSmix.
The superconducting properties for (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex are shown in Figure 6(c). A superconducting transition with Tc > 2 K was observed for x = 0 and 0.25. By focusing on these two phases, interesting trend was found. Although the Tc for x = 0.25 is lower than that for x = 0, the suppression of Tc for x = 0.25 under magnetic fields is clearly smaller than that for x = 0. From the estimation of upper critical field (Hc2), it was found that the Hc2 (0 K) for x = 0.25 is higher than that for x = 0. In addition, from the measurements of the magnetization-field loop, it was confirmed that the critical current density (Jc) at 1.8 K for x = 0.25 is larger than that for x = 0. These results suggest that an increase in ΔSmix may be useful to improve Hc2 and/or Jc characteristics of superconductors if the problem on the suppression of Tc could be solved.
3. CuAl2-type TrZr2
As shown in the last section, high-entropy alloying of a compound, which possesses two or more crystallographic sites, is a route to develop new superconductors with a high mixing entropy. In addition, in HEA-type compounds, not only the site entropy but also the entropy of chemical bonding states should be higher than normal alloys or compounds. To discover new HEA-type superconductors, the use of material database is quite useful. SuperCon (NIMS database)  is a database of superconductors and contain information of composition, structural type, Tc, and reference of the material. To achieve the material design of HEA-type superconductors, we have to find a system in which compositional variation is rich within the same structural type, and superconducting transition has been observed. Herein, we introduce an example of material design for new HEA-type superconductors.
TrZr2 (Tr: transition metal) with a tetragonal CuAl2-type structure (Figure 4(c)) is a superconducting system. For Tr = Fe, Co, Ni, Rh, Ir, superconductivity was reported. Among them, CoZr2, RhZr2, and IrZr2 exhibits a higher Tc of 5.5, 11.3, and 7.5 K, respectively . Furthermore, the Tr site can be partially substituted by Sc, Cu, Ga, Pd, and Ta [34, 45]. These facts suggest that the Tr site of TrZr2 can be modified into a HEA-type site. We synthesized Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 by arc melting and observed superconductivity with a Tc of 8 K . The Tr site of Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 contains five transition metals, and the ΔSmix for the Tr site is about 1.5R. In addition, (Fe,Co,Ni,Rh,Ir)Zr2 superconductors were also synthesized and exhibited superconductivity . Interestingly, the resulting Tc in HEA-type phases was very close to the weighted-average Tc of pure TrZr2 systems. Although the origin of the unexpected behavior is still unclear, the effects of disordering by the HEA-type site to superconducting properties seem very limited. The difference in the HEA effects between MCh and TrZr2 may be caused by the different structural complexity.
As shown in Figure 7(a), the temperature dependence of resistivity exhibits a relatively large RRR as compared to other HEA-type superconductors. However, a large RRR of ~30 was reported for CoZr2 single crystals , which is clearly larger than that for HEA-type TrZr2. Therefore, the HEA effects (disordering effects) to transport properties would be a common trend. Figure 7(b) shows the temperature dependences of the specific heat for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 in the form of C/T. Although a clear jump of C/T at the Tc is seen, the transition is broader as compared to the case of CoZr2. The trend of broad transition in specific heat at Tc was not observed in a HEA superconductor but observed in HEA-type compounds. Because the superconducting transitions observed in resistivity and magnetization were sharp, the broad transition in the specific heat would suggest microscopic local phase separation in HEA-type superconducting compounds.
4. Cuprate (high-Tc) superconductors REBa2Cu3O7-d
As mentioned in introduction, cuprates (Cu oxides) have been extensively studied in the fields of science and engineering because of its high Tc. Among them, REBa2Cu3O7-d (RE123) system  is one of practical materials for superconductivity application. In addition, a high Jc was reported in RE123 samples with three elements at the RE site . Motivated by the fact, we synthesized polycrystalline samples of REBa2Cu3O7-d with different ΔSmix for the RE site  by standard solid-state reaction in air. In the study, two-step annealing was performed to optimize oxygen content (d) because oxygen content affect crystal structure (orthorhombicity) and superconducting properties of REBa2Cu3O7-d. A high superconducting property is generally achieved in an orthorhombic phase in the system, we estimated the orthorhombicity parameter (OP), which is given by 2|a-b|/(a + b), and plotted the estimated Tc and magnetic Jc (T = 2 K, B = 1 T) for REBa2Cu3O7-d as a function of OP as shown in Figure 8. Note that the data points are colored according to the number of elements contained at the RE site. From the plot, it is found that Tc does not show a remarkable correlation with ΔSmix (RE site) and exhibits a clear correlation with OP. Jc also exhibits a trend of improvement with increasing OP. These facts suggest that disorder introduced by high-entropy alloying at the RE site (see Figure 4(d)) does not largely affect superconducting properties of REBa2Cu3O7-d, which is a two-dimensional layered compound. Because the trend is clearly different to that observed for cubic (NaCl-type) tellurides with a HEA-type site, crystal-structure dimensionality is a key factor to how the introduction of HEA-type site affects superconducting properties in compounds.
In Figure 8(b), we found three data points for HEA-type samples show a Jc larger than that for the other low-entropy samples at OP = 0.01–0.015. Although it has not been fully clarified whether the slightly large Jcs in the HEA-type samples are caused by high-entropy alloying or not, the effect of high-entropy alloying for cuprates should be further studied to find the way to improve practical performance of cuprate superconductors.
5. BiS2-based layered superconductors RE(O,F)BiS2
BiS2-based superconductor family is one of the layered superconductor families and was discover in 2012 [49, 50, 51]. The crystal structure is composed of alternate stacks of a conducting BiS2 bilayer and a blocking layer (for example, a REO layer), which is similar to that of high-Tc systems. Furthermore, unconventional superconductivity has been proposed from theoretical and experimental studies on the BiS2-based compounds .
A typical BiS2-based system is REOBiS2 (see Figure 4(e)). Because non-doped REOBiS2 is a semiconductor, electron carrier doping is required to induce metallicity . For RE = La, a superconducting transition was observed at 2.5 K after electron doping through partial substitution of O by F in LaO0.5F0.5BiS2. However, the superconductivity states in La(O,F)BiS2 is not bulk in nature. This is due to the presence of the local disorder due to Bi lone pairs, and the local disorder could be suppressed by in-plane chemical pressure effects [52, 53, 54]. In-plane chemical pressure can be generated by RE-site substitution by smaller RE ions or Se substitution for the S site. By increasing in-plane chemical pressure, local disorder is suppressed, and bulk superconductivity is induced [52, 53]. Therefore, one can say that RE(O,F)BiS2 is a useful system to investigate the effect of structural modification on local crystal structure and superconducting properties. This suggests that the investigation of the effects of introduction of a HEA site in RE(O,F)BiS2 would provide us with key information about interlayer interaction through the HEA states.
The HEA-type samples of REO0.5F0.5BiS2 with RE = La, Ce, Pr, Nd, Sm were synthesized by solid-state reaction in an evacuated quartz tube . Figure 9(a) and (b) show superconducting properties of four different HEA-type REO0.5F0.5BiS2 samples. The Tc varies depending on the RE-site composition. As shown in Figure 9(c), these four samples have different lattice constants a, which is corresponding to different in-plane chemical pressures. Therefore, the variation of Tc can be understood with the in-plane chemical pressure scenario. When focusing on the samples with the same lattice constant a and different mixing entropy, we find that the superconducting properties (Tc and Δ4πχ) of the HEA-type sample are higher than those of low-entropy samples (Figures 9(c) and (d)). The facts indicate that an increase in ΔSmix for the RE site may positively work in improving superconducting properties. Therefore, we systematically prepared REO0.5F0.5BiS2 samples with the same lattice constant a and different ΔSmix to investigate the interlayer interaction .
As summarized in Figure 10(a), we succeeded in preparation of a set of five REO0.5F0.5BiS2 samples with almost the same a and systematically varied ΔSmix. Because the lattice constant a nearly corresponds to the degree of the in-plane chemical pressure, the set of samples have almost similar in-plane chemical pressure. Therefore, we could detect the effects of the increase in ΔSmix to superconducting properties and local structural disorder . Through magnetic susceptibility measurements, we confirmed that shielding volume fraction increases with increasing ΔSmix while the Tc does not change (Figure 10(c) and (d)). To understand the origin of the improvement of superconducting properties, local structure was analyzed using synchrotron X-ray diffraction. As summarized in Figure 10(b), suppression of in-plane structural disorder, which was detected by anisotropic displacement parameter for the in-plane direction (U11), was achieved by the HEA effect at the RE site. Similar trend was observed in another set of REO0.5F0.5BiS2 samples with larger lattice constant (comparable to that of CeO0.5F0.5BiS2). The results propose that high-entropy alloying at the blocking layer would modify the local structure at the conducting layer in BiS2-based layered compounds. This effect should be a new strategy to develop novel functional materials with a layered structure.
In this chapter, we reviewed the works on HEA superconductors and HEA-type superconducting compounds, which have been developed applying the HEA concept in simple alloys to more complicated compounds. By introducing a HEA-type site (or alloying multi sites) in a compound, a high mixing entropy can be achieved. HEA-type compounds would have a high mixing entropy at the alloyed site and a highly (randomly) disordered bonding states. For a three-dimensional system, such as NaCl-type chalcogenides, introduction of the HEA-type M site in MCh resulted in suppression of Tc, but, at the same time, slight enhancements of Hc2 and Jc were observed. For tetragonal (CuAl2-type) TrZr2, the introduction of the HEA-type site does not suppress Tc. Furthermore, for layered systems, such as REBa2Cu3O7-d cuprates and BiS2-based RE0.5F0.5BiS2, high-entropy alloying rather improves their superconducting properties. Through investigations of the HEA effects to superconducting and structural properties for HEA-type compounds with different structural types, we conclude that the HEA effects are highly depending on the structural dimensionality. Hence, to effectively use the HEA effect to improve superconducting properties of compounds, target structure should be lower-symmetric, a layered structure or a one-dimensional structure. To obtain further knowledge about the presence/absence of local phase separations, pinning characteristics, and the HEA effect to superconducting pairing states, further investigations on HEA-type superconducting compounds using various probes are required.
The author thanks R. Sogabe, Md. R. Kasem, Y. Shukunami, M. Katsuno, K. Hoshi, R. Jha, Y. Goto, T. D. Matsuda, and O. Miura who have contributed on the works reviewed here. The author would like to thank all the coauthors of the works. The works reviewed here were supported by JSPS-KAKENHI (Nos.: 16H04493, 15H05886, 18KK0076), JST-CREST (Nos.: JPMJCR16Q6, JPMJCR20Q4), and Tokyo Metropolitan Government Advanced Research (No.: H31-1).