We report on a novel TaNbZrHfTi-based high entropy alloy (HEA) which demonstrates distinctive dual-phase superconductivity. The HEA was synthesized under high pressures and high temperatures starting from a ball milled mixture of elemental metals in a large-volume Paris–Edinburgh cell with P ≈ 6 GPa and T = 2300 K. The synthesized HEA is a phase mixture of BCC (NbTa)0.45(ZrHfTi)0.55 with Tc1 = 6 K and FCC (NbTa)0.04(ZrHfTi)0.96 with Tc2 = 3.75 K. The measured magnetic field parameters for the HEA are lower critical field, Hc1(0) = 31 mT, and a relatively high upper critical field, Hc2(0) = 4.92 T. This dual-phase system is further characterized by the presence of a second magnetization peak, or the fishtail effect, observed in the virgin magnetization curves. This phenomenon, which does not distort the field-dependent magnetization hysteresis loops, suggests intricate pinning mechanisms that could be potentially tuned for optimized performance. The manifestation of these unique features in HEA superconductivity reinforces phase-dependent superconductivity and opens new avenues in the exploration of novel superconducting materials.

High entropy alloys (HEAs), comprising five or more principal elements in equimolar or near-equimolar ratios, represent a significant shift from traditional alloys. They achieve a high contribution of configurational entropy to Gibbs free energy, which stabilizes robust high-symmetry phases, thereby offering novel perspectives in alloy design.1–3 Such materials have paved the way for a wide range of significant technological applications, excelling over many traditional materials in fields such as aerospace, mechanical manufacturing, biomedicine, and energy development due to their unique physical, chemical, and mechanical properties.4–6 

The complex nature of HEAs offers intriguing challenges and provides fresh perspectives to our conventional understanding of material physics, particularly regarding phase stability in multi-component systems. For example, HEAs comprising elements such as Ta, Nb, Hf, Zr, and Ti have demonstrated unexpected structural anomalies. These include the formation of inter-grain phases (IGPs) with unique compositions and distinct crystalline structures. A notable instance of such an anomaly is an IGP exhibiting a face-centered cubic (FCC) crystal structure.3 This finding is particularly surprising as the phase diagrams of these constituent elements typically display only body-centered cubic (BCC) and hexagonal close-packed (HCP) structures. Such deviations from the expected behavior challenge existing theoretical frameworks and prompt a re-evaluation of phase formation dynamics in these complex systems.

HEAs have also made a significant impact in the realm of superconductivity with the discovery of the first HEA superconductor, the BCC alloy Ta34Nb33Hf8Zr14Ti11, in 2014.7 This landmark discovery spurred subsequent studies that explored a wide array of HEA superconductors, encompassing a broad spectrum of structural types such as BCC, HCP, CsCl-type, A15, NaCl-type, α (or β)-Mn-type, σ-phase type, CuAl2-type, W5Si3-type, BiS2-based, and YBCO-based structures.8 These investigations primarily revealed conventional s-wave Bardeen–Cooper–Schrieffer (BCS) type superconducting properties.9 A distinctive aspect of certain BCC alloys, such as Nb-Re-Hf-Zr-Ti and Ta-Nb-Hf-Zr-Ti, is their short electronic mean free path compared to their BCS coherence lengths, placing them in the “dirty limit” regime due to considerable atomic disorder.10 Furthermore, these alloys exhibit high critical current densities in both bulk and thin film forms. Ta-Nb-Hf-Zr-Ti films have demonstrated critical current densities exceeding those of conventional high-field superconducting magnets.11 Moreover, their superconducting layers display remarkable robustness under ion irradiation, suggesting their potential for high-endurance applications. In addition, superconducting HEAs have shown unexpected and robust zero-resistance superconductivity across an extraordinarily wide range of pressures.12,13 For example, the (TaNb)0.67(HfZrTi)0.33 alloy displays a peculiar behavior where the superconducting transition temperature (Tc) increases from 7.7 K at ambient pressure to 10 K around 60 GPa before dropping to 9 K at 190.6 GPa. This unusual behavior, particularly in a material with a complex electronic structure, raises intriguing questions about the mechanisms driving superconductivity in these alloys.14 Meanwhile, the robustness of superconductivity under high pressure is emerging as a universal characteristic in HEA-type superconductors.13 

In response to these advancements in the field of high entropy alloys, our study delves into the superconducting behavior of a TaNbZrHfTi-based HEA. Through a synthesis process utilizing a large volume Paris–Edinburgh press, we have successfully created a material that exhibits superconductivity in both BCC and FCC phases. To thoroughly investigate the properties of this unique and complex material, we employed a combination of x-ray diffraction (XRD), scanning electron microscopy (SEM), and vibrating sample magnetometry (VSM) techniques.

The TaNbZrHfTi-based high entropy alloy, described by the formula (TaNb)1−x(ZrHfTi)x, was synthesized using the large-volume Paris–Edinburgh (PE) press at the High-Pressure Collaborative Access Team (HPCAT) facility of the Advanced Photon Source (APS), Argonne National Laboratory (ANL). Stoichiometric amounts of Ta, Nb, Zr, Hf, and Ti (all with purities of 99.9% or higher) were weighed out for the composition (TaNb)0.67(HfZrTi)0.33 and then ball milled for 6 h in a Spex 8000M high-energy mill under an argon atmosphere, which was maintained by sealing the milling media in a glove box with less than 1 ppm of O2 and H2O. The ball-to-powder weight ratio was set at 10:1, and a specific ball-to-sample weight ratio of 1.04 was used to ensure effective impact and mixing during milling. The mill operates at a fixed rotational speed, typical of the Spex 8000M model, which is ∼1200 rpm. The milled powder was sieved through a 400-mesh sieve and loaded into a sealed vial to maintain the argon environment. For synthesis, the sample was compressed into a 1.5 mm diameter by 2 mm tall cylinder and placed in a standard PE press cell, surrounded by a hexagonal boron nitride (hBN) capsule. The cell was then placed inside the PE press and subjected to 12 000 psi via a hydraulic press (for more details, see Refs. 15 and 16). After stabilizing the pressure, the sample was heated to 2300 K over 30 min using a graphite heater. The sample was left to soak at maximum pressure (6–8 GPa) and temperature (2300 K) for 30 min before being quenched, with a cooling rate of ∼34 K/s down to around 600 K. Using this technique, several samples were produced, which later revealed the same characteristics.

To prepare the sample for analysis, post-synthesis grinding and polishing were necessary to remove hBN contamination from the surface. Using SiC sandpaper and subsequent diamond pastes of varying sizes, the samples were polished to a mirror finish, enabling the distinction of separate phases in microscopy analysis.

The crystalline structure of the synthesized material was analyzed using a PANalytical Empyrean x-ray diffractometer. A Cu-Kα anode (λ = 1.541 86 Å) was used with power resulting from 45 kV to 40 mA settings. The XRD data were analyzed using HighScore Plus, and Le Bail refinements were performed using the JANA2020 software.17 

The sample compositions and surface morphology were investigated by Scanning Electron Microscopy coupled with Energy-Dispersive Spectroscopy (SEM-EDS). The data were acquired with a Quanta FEG 650 scanning electron microscope. This analysis enabled detailed observation of the surface characteristics of the high entropy alloy, revealing the distinct phases and providing insight into the microstructural features of the material.

The superconducting properties of the samples were analyzed using the Vibrating Sample Magnetometer (VSM) technique within a Quantum Design Physical Property Measurement System (PPMS) DynaCool. This technique hinges on the measurement of magnetic flux changes, which occur due to the periodic motion of a sample within a uniformly applied magnetic field (H). These changes in magnetic flux from the sample are accurately detected by sensing coils. This technique is used to explore the temperature dependence of magnetic moment, as well as to chart the magnetization vs magnetic field (M-H) loops at various temperatures.

Figure 1 presents the powder x-ray diffraction (XRD) pattern for a high-pressure-temperature synthesized (TaNb)1−x(ZrHfTi)x HEA. The indexing of the XRD pattern indicated that the material consists of two phases: a BCC structure (space group Im3̄m) and an FCC structure (space group Fm3̄m). The quantitative analysis utilizing the Le Bail method shows that 74.5% of the material consists of the BCC phase, while 25.5% comprises the FCC phase. These percentages represent the weight percentages of each phase, indicating the relative mass of each phase as a proportion of the total mass of the sample. The lattice parameter estimated for the BCC phase was found to be a = 3.373 Å, falling within the range of the (TaNb)1−x(ZrHfTi)x system, where the unit cell parameter is found to vary from about 3.33 to 3.43 Å.14 In the case of the FCC structure, the lattice parameter a is 4.545 Å and consistent with the lattice parameter for the inter-granular FCC phase reported in earlier studies.3 The emergence of the FCC phase can be closely linked to the specific conditions under which the alloy was prepared. It is known that the atmosphere during the milling process plays a critical role in phase formation. While our process was conducted under an argon atmosphere to prevent contamination, the literature indicates that different atmospheres, particularly those involving nitrogen and oxygen, can affect the stabilization of distinct phases, including the FCC phase, in similar high-entropy alloys.18 This underscores the importance of controlled atmospheric conditions during preparation to achieve the desired phase outcomes in high-entropy alloys.

FIG. 1.

X-ray diffraction pattern of the TaNbZrHfTi-based high entropy alloy. The experimental data (red dots) are well-fitted by the refinement (black line), with the difference plot (blue line) indicating the quality of the fit. The identified peaks are marked for the body-centered cubic (BCC, green vertical lines) and face-centered cubic (FCC, purple vertical lines) phases. The background signal is represented by the lower gray line.

FIG. 1.

X-ray diffraction pattern of the TaNbZrHfTi-based high entropy alloy. The experimental data (red dots) are well-fitted by the refinement (black line), with the difference plot (blue line) indicating the quality of the fit. The identified peaks are marked for the body-centered cubic (BCC, green vertical lines) and face-centered cubic (FCC, purple vertical lines) phases. The background signal is represented by the lower gray line.

Close modal

The actual appearance of the alloy, as shown in Fig. 2(a), after synthesis, exhibits a metallic gray surface. As described in the Methods section, samples were well-polished for SEM-EDS analysis. The compositional analysis via EDS aligns with the XRD results, confirming the coexistence of BCC and FCC structures within the alloy. The SEM image in Fig. 2(b) shows the presence of two contrasting regions that are indicative of the phases mentioned within the material. The darker regions, identified by EDS spot 1, correspond to the FCC phase, characterized by a higher content of Zr, Hf, and Ti. In contrast, the lighter areas, marked by EDS spot 2, denote the BCC phase with a richer concentration of Nb and Ta. The distinction between the two phases is stark, emphasizing the successful integration of diverse elements into a single, multi-phase material.

FIG. 2.

Microscopic characterization of the TaNbZrHfTi-based high entropy alloy. (a) Optical image of the sample after synthesis. (b) SEM image of the polished sample surface highlighting the two distinct phases identified by EDS. EDS spot 1 (red) corresponds to the darker FCC phase, and EDS spot 2 (cyan) corresponds to the lighter BCC phase, evidencing the dual-phase nature of the alloy.

FIG. 2.

Microscopic characterization of the TaNbZrHfTi-based high entropy alloy. (a) Optical image of the sample after synthesis. (b) SEM image of the polished sample surface highlighting the two distinct phases identified by EDS. EDS spot 1 (red) corresponds to the darker FCC phase, and EDS spot 2 (cyan) corresponds to the lighter BCC phase, evidencing the dual-phase nature of the alloy.

Close modal

From SEM-EDS data, the averaged and normalized percentages of elements indicate that the BCC composition is (NbTa)0.45(ZrHfTi)0.55 and the FCC composition is (NbTa)0.04(ZrHfTi)0.96. These results suggest that the FCC structure is stable at high concentrations of Zr, Hf, and Ti. It is noteworthy that the specific arrangements of phases, and the nature of their interfaces, play an important role in determining the overall material properties. For example, in the case of HEAs doped with small amounts of aluminum, structural transitions from FCC to dual-phase FCC + BCC, and eventually to a single BCC phase, have been observed.19,20

Figure 3 shows the temperature-dependent magnetization of the HEA under zero-field-cooled (ZFC) and field-cooled (FC) conditions. The ZFC curve reveals a prominent superconducting transition with an onset temperature Tc1 = 6 K, which is linked to the dominant BCC phase, a finding supported by our SEM and XRD results. A second, more subtle transition at Tc2 = 3.75 K emerges on the FC curve, suggestive of a secondary superconducting phase. To ensure the authenticity of this delicate feature and to rule out any technical failures of the device, the sample was repeatedly measured, confirming its reproducibility (see Fig. S1 in the supplementary material). These repeated measurements consistently demonstrated the drop in the FC curve. This drop in magnetization aligns with the FCC phase, which occupies a lesser volume fraction within the material. The distinction between the ZFC and FC behaviors below Tc2 is indicative of the FCC phase’s superconductivity and its interaction with the primary BCC phase. The sustained diamagnetic signal in the ZFC curve down to the lowest temperatures in this work confirms the presence of superconductivity. The FCC phase, although secondary, contributes to the overall superconducting properties and the complexity observed in the magnetization behavior.

FIG. 3.

Temperature dependence of magnetization in a ZFC–FC protocol for the high entropy alloy with BCC and FCC superconducting phases, measured at H = 20 Oe. The inset reveals the transition of the FCC phase at 3.75 K, distinguishing it from the BCC phase transition at 6 K.

FIG. 3.

Temperature dependence of magnetization in a ZFC–FC protocol for the high entropy alloy with BCC and FCC superconducting phases, measured at H = 20 Oe. The inset reveals the transition of the FCC phase at 3.75 K, distinguishing it from the BCC phase transition at 6 K.

Close modal

Figure 4(a) presents the virgin magnetization curves of the HEA, featuring a two-peak effect at various temperatures. The initial peak (peak A) is associated with the lower critical field Hc1 and shows a decrease in field strength as the temperature increases, reflecting the alloy’s transition from a complete Meissner state to a mixed state. The second peak (peak B) is particularly interesting as it is indicative of the fishtail effect, a complex feature often found in type-II superconductors.21–23 The consistency of peak B with Tc2 = 3.75 K, previously noted in Fig. 3, affirms its interpretation as a superconducting transition associated with the FCC phase. Exclusively appearing in the virgin state, this effect signals the unique pinning characteristics of the HEA before any field cycling occurs. A similar effect was reported in Ti-Hf-Nb-Ta-Re superconducting alloys, which demonstrate phase segregation into two BCC phases with slightly different chemical compositions.24 On the other hand, the absence of the fishtail effect in the M-H hysteresis loops [Fig. 4(b)] implies that initial magnetic penetration modifies the vortex dynamics, which are further transformed by subsequent magnetic field cycling. This could lead to potential avenues for tailoring superconducting properties via controlled magnetic history. The exclusive presence of the two-peak structure in the virgin curves of a single material is not only a fascinating scientific observation but also has potential ramifications for the development of superconducting materials. It hints at a superconducting phase that can be optimized for improved critical current densities or augmented field resilience, both of which are essential for practical superconducting applications.

FIG. 4.

Magnetization vs magnetic field curves at selected temperatures, highlighting the superconducting properties of the material. (a) The virgin magnetization curves exhibit two pronounced peaks (labeled as A and B in the inset), indicative of intricate pinning mechanisms within the mixed superconducting state. (b) The full magnetization hysteresis, M-H, loops, capturing the reversible and irreversible magnetization processes associated with the BCC and FCC superconducting phases of the alloy.

FIG. 4.

Magnetization vs magnetic field curves at selected temperatures, highlighting the superconducting properties of the material. (a) The virgin magnetization curves exhibit two pronounced peaks (labeled as A and B in the inset), indicative of intricate pinning mechanisms within the mixed superconducting state. (b) The full magnetization hysteresis, M-H, loops, capturing the reversible and irreversible magnetization processes associated with the BCC and FCC superconducting phases of the alloy.

Close modal

Similar to our TaNbZrHfTi-based alloy, (TaNb)0.7(HfZrTi)0.5 also demonstrates the fishtail effect in its magnetization curves, characteristic of complex vortex pinning mechanisms seen in high-entropy alloys.8 However, unlike our material, which supports both BCC and FCC phases, the (TaNb)0.7(HfZrTi)0.5 alloy exhibits this behavior only after specific heat treatments and does not show FCC phase formation. This highlights the critical role that synthesis and processing conditions play in phase formation and the resultant superconducting properties of high-entropy alloys. An interesting comparison arises when considering a recent study on a Th-containing high-entropy alloy superconductor, nominally composed of (NbTa)0.67(MoWTh)0.33.25 The significance of this earlier study lies in the 5f-electron states of thorium, which are anticipated to impart distinct magnetic behaviors to the alloy. Although this alloy also featured a dominant BCC phase and a minor FCC phase, the second magnetization peak was not observed in magnetic measurements. (NbTa)0.67(MoWTh)0.33 exhibits superconducting transitions at 7 and 5.6 K. The extrapolated zero-temperature lower and upper critical fields were estimated to be 3.4 mT and 0.73 T, respectively. These findings highlight the influence of chemical composition on superconducting properties, particularly in the context of thorium’s unique electron states.

Figure 5 elucidates the temperature-dependent evolution of the two-peak effect, showcasing the lower critical field Hc1(T) and upper critical field Hc2(T) trends in the HEA. The temperature dependencies of Hc1(T) and Hc2(T), illustrated in Figs. 5(b) and 5(c), respectively, were analyzed using the magnetic field vs magnetization data collected at various temperatures using VSM. The theoretical framework for these dependencies is provided by the Ginzburg–Landau (GL) theory, referenced in Refs. 26 and 27, which offers a robust model for describing superconducting phase transitions under external magnetic fields. The lower critical field Hc1(T), indicating the onset of magnetic flux penetration into the superconductor, is modeled by the following formula:
Hc1T=Hc1(0)(1t2),
(1)
where t = T/Tc represents the reduced temperature, corresponding to the deviation from the Meissner state (complete diamagnetism). The upper critical field Hc2(T), indicating the field at which magnetization rapidly drops to zero (transition from the superconducting state to the normal state), is given by
Hc2T=Hc201t21+t2.
(2)
These formulas, depicted by the dashed lines in the figures, allow us to extrapolate the zero-temperature critical fields Hc1(0) and Hc2(0).
FIG. 5.

Temperature variation in the two-peak behavior, lower, Hc1, and upper, Hc2, critical fields for the HEA. (a) The evolution of peaks A and B, which are linked to the distinct superconducting properties of the mixed BCC and FCC phases (see more details in Fig. S2). (b) and (c) Critical fields, Hc1 and Hc2, respectively, against the reduced temperature, T/Tc. The dashed lines represent the GL theoretical fits, which extrapolate to the zero-temperature critical fields.

FIG. 5.

Temperature variation in the two-peak behavior, lower, Hc1, and upper, Hc2, critical fields for the HEA. (a) The evolution of peaks A and B, which are linked to the distinct superconducting properties of the mixed BCC and FCC phases (see more details in Fig. S2). (b) and (c) Critical fields, Hc1 and Hc2, respectively, against the reduced temperature, T/Tc. The dashed lines represent the GL theoretical fits, which extrapolate to the zero-temperature critical fields.

Close modal

The persistent manifestation of peaks A and B, correlated with the BCC and FCC superconducting phases, illustrates the detailed temperature landscape of the material’s superconducting state. Despite the alloy comprising two distinct phases, the GL theory provides an accurate description, yielding zero-temperature critical fields Hc1(0) and Hc2(0) of 31 mT and 4.92 T, respectively, as depicted in Figs. 5(b) and 5(c). From these values, the thermodynamic critical field Hc(0) can be estimated as Hc0=Hc10Hc20, yielding ∼0.39 T. This value represents a critical parameter in assessing the robustness and stability of the superconducting state under external magnetic fields. The application of GL theory, typically used for homogeneous materials, suggests a level of comparative uniformity in superconducting properties across the different phases in this high-entropy alloy. This comparative uniform superconducting response, characterized by these critical fields, further supports the presence of robust superconducting states within the mixed-phase structure of the HEA.

To further characterize the superconducting state, the London penetration depth λ(0) and the GL coherence length ξ(0) were estimated using the critical magnetic fields at zero temperature, Hc1(0) and Hc2(0), derived from the following relationships:
Hc10=Φ04πλ2lnλξ,
(3)
Hc20=Φ02πξ2,
(4)
where Φ0 is the magnetic flux quantum, given by Φ0 = h/2e. These equations allow for the quantification of the superconducting screening ability (Hc1) and the field at which superconductivity is destroyed (Hc2), providing insight into the superconducting states within the mixed-phase structure of the HEA.

The London penetration depth, λ(0), is calculated to be 132 nm, and the GL coherence length, ξ(0), is calculated to be ∼8.18 nm. Therefore, the GL parameter κ = λ(0)/ξ(0) is ∼16.1. This value of κ>1/2 confirms that the alloy is a type-II superconductor, aligning with the observed high critical field Hc2(0). All parameters are summarized in the supplementary material.

While the congruent description provided by GL theory for our HEA containing both BCC and FCC phases is intriguing, it warrants cautious interpretation. This congruity suggests that while the distinct crystal structures and the associated electronic environments may have individual characteristics, the macroscopic superconducting properties reflected in critical fields are effectively captured by GL theory for both phases. The potential benefits of such congruity in superconducting properties include the possibility of an enhanced critical current density over a wider range of temperatures and fields than would be possible with a single-phase material. If the superconducting gaps of both phases are similar, or if one phase can sustain superconductivity under conditions where the other might not, the material could exhibit superior performance, which is desirable in applications requiring high critical currents or stability against thermal fluctuations. Furthermore, the dual-phase nature presents intrinsic heterogeneity that may act as effective pinning centers for vortices, which could potentially lead to a high vortex pinning force and hence a high critical current. This aspect could be particularly advantageous in magnetic field applications, such as in magnetic resonance imaging (MRI) machines or particle accelerators, where maintaining a high current in a high magnetic field is crucial.

In the classification of HEAs as superconductors, the Valence Electron Count (VEC) is an important factor. For a multi-component alloy, the VEC is calculated using a weighted average formula:28,29 VEC=i=1nci×VECi, where ci is the atomic fraction (or concentration) of each element in the alloy and VECi is the valence electron concentration of each element. This method considers the varying proportions of each element, facilitating the classification of HEAs into distinct categories based on their respective VEC values, transition temperatures, and crystalline structures:14,28–32

  • Type-A HEAs, which crystallize in a BCC lattice, typically have a VEC range from 4.3 to 4.8.

  • Type-B HEAs, forming in an α-Mn lattice, exhibit superconductivity within a VEC range of 6.5 to over 6.8.

  • Type-C HEAs are characterized by a CsCl lattice structure and have VECs ranging approximately from 5.8 to 6.3.

  • Type-D HEAs, crystallizing in an HCP lattice, typically possess VECs within the range 5.2–5.8.

In this context, our BCC (NbTa)0.45(ZrHfTi)0.55 and FCC (NbTa)0.04(ZrHfTi)0.96, having VECs of 4.45 and 4.04, respectively, align with the type-A classification and are closely associated with the mentioned VEC diagrams for superconducting transition temperatures. However, the positioning of the FCC phase in the VEC diagram is complex and subject to debate. While conventional guidelines indicate that HEAs with a VEC higher than 7.8 tend to stabilize in an FCC structure and those with a VEC lower than 6.87 tend to stabilize in a BCC structure,29,32 these rules are not absolute. This is exemplified in Ref. 3, which describes an FCC IGP within a predominantly BCC structured HEA that does not conform to the usual threshold for FCC formation. Moreover, our HEA, exhibiting an FCC phase with a VEC of 4.04, further challenges these conventional guidelines. This finding underscores that while VEC is instrumental in predicting phase stability, it may not be the sole determinant. Other influences, such as atomic size, electronegativity, and mixing entropy, could also play significant roles in phase formation. In the case of our HEA with an FCC phase VEC of nearly 4, this suggests that factors beyond the VEC are contributing to its stabilization in an FCC structure, indicating the need for a more nuanced interpretation of VEC diagrams in HEAs.

In this study, we presented a novel TaNbZrHfTi-based high entropy alloy exhibiting dual-phase superconductivity in the (TaNb)1−x(ZrHfTi)x-type system. Notably, this alloy demonstrates a unique coexistence of BCC and FCC phases made possible by high-pressure high-temperature synthesis, a composition that has not been previously reported in the (TaNb)1−x(ZrHfTi)x system. Previous observation of the FCC phase in this system has been limited to thin films or intergranular phases (IGPs) but not as a bulk phase reported in this paper. We show that the BCC (NbTa)0.45(ZrHfTi)0.55 phase, with Tc1 = 6 K, and the FCC (NbTa)0.04(ZrHfTi)0.96 phase, with Tc2 = 3.75 K, contribute distinctly to the overall superconducting behavior. This material maintains typical HEA parameters, including a lower critical field, Hc1(0) = 31 mT, and a relatively high upper critical field, Hc2(0) = 4.92 T, positioning it within the type-A classification on the VEC diagram. The congruent superconducting characteristics across both phases underline a unique synergy within this complex alloy system. Our findings not only offer fresh insights into phase interactions and superconductivity in HEAs but also underscore the potential of these materials in demanding applications. This research contributes to the rapidly evolving field of HEAs, indicating promising avenues for future studies aimed at unlocking the full potential of these advanced materials in both fundamental science and technological applications.

See the supplementary material for details on magnetization measurements, elemental concentrations determined by EDS, and characteristic parameters of normal and superconducting states for the TaNbZrHfTi-based high-entropy alloy.

This material is based on the work supported by the National Science Foundation (NSF), under Grant No. DMR-2310526. The Physical Properties Measurements System (PPMS) employed in this study was acquired under NSF MRI Grant No. 2215143. Portions of this work were performed at HPCAT (Sector 16), Advanced Photon Source, Argonne National Laboratory. HPCAT operations are supported by DOE-NNSA’s Office of Experimental Sciences. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

The authors have no conflicts to disclose.

Raimundas Sereika: Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (lead); Writing – review & editing (equal). Seth Iwan: Formal analysis (equal); Methodology (equal). Paul A. Baker: Formal analysis (equal); Methodology (equal). Wenli Bi: Funding acquisition (equal); Methodology (equal); Writing – review & editing (equal). Yogesh K. Vohra: Conceptualization (equal); Funding acquisition (equal); Project administration (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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