pith. sign in

arxiv: 2605.25048 · v1 · pith:HOJ3LVH2new · submitted 2026-05-24 · ❄️ cond-mat.supr-con

Superconductivity in Al-based high-entropy alloys TiHfNbTaAl and TaNbHfZrAl

Junjin Huang , Wenbo Sun , Longfu Li , Shuangyue Wang , Jingjun Qin , Rui Chen , Zaichen Xiang , Yucheng Li
show 2 more authors
Lingyong Zeng Huixia Luo
This is my paper

Pith reviewed 2026-06-29 23:48 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords high-entropy alloyssuperconductivitytype-II superconductorsbody-centered cubicvalence electron concentrationTaNbHfZrAlTiHfNbTaAldisordered metals
0
0 comments X

The pith

Two Al-based high-entropy alloys are bulk type-II superconductors with Tc of 5.5 K and 3.2 K.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the electrical resistivity, magnetic response, and specific heat of the high-entropy alloys TaNbHfZrAl and TiHfNbTaAl. Both alloys form a body-centered cubic structure with valence electron count 4.2 and show zero-resistance transitions at 5.5 K and 3.2 K respectively. The data establish that the transitions are bulk and type-II in character. Aluminum incorporation produces a Tc dependence that resembles crystalline rather than highly disordered systems. A sympathetic reader would care because these materials test how strong chemical disorder affects superconductivity in the intermediate regime between crystals and glasses.

Core claim

TaNbHfZrAl and TiHfNbTaAl high-entropy alloys both crystallize in the body-centered cubic structure with valence electron count 4.2. Resistivity, magnetic, and specific heat measurements establish that they are bulk type-II superconductors with critical temperatures of 5.5 K for TaNbHfZrAl and 3.2 K for TiHfNbTaAl. The Tc of HEA superconductors depends on valence electron count and element composition, and aluminum incorporation yields a more crystalline-like Tc dependence.

What carries the argument

Body-centered cubic high-entropy alloy lattice with valence electron count fixed at 4.2, where multi-element disorder and aluminum content together set the superconducting transition temperature.

If this is right

  • The critical temperature in these alloys is controlled by the valence electron count and the specific choice of elements.
  • Aluminum addition shifts the Tc dependence toward the behavior seen in crystalline superconductors.
  • Both alloys display type-II superconductivity with bulk character verified by three independent probes.
  • High-entropy alloys with VEC near 4.2 provide a tunable platform for superconductivity in highly disordered metals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Systematic changes in aluminum fraction could map how disorder strength affects the superconducting transition width and gap.
  • The reported Tc values supply concrete benchmarks for models that relate valence electron count to pairing strength in random alloys.
  • Compositions built from the same refractory metals might be screened for higher Tc while preserving the BCC high-entropy structure.

Load-bearing premise

The resistivity drop, magnetic response, and specific heat anomaly all arise from the same bulk superconducting phase in the main high-entropy alloy rather than from minor impurity phases or surface effects.

What would settle it

Detection of impurity phases by x-ray diffraction or additional specific-heat anomalies at temperatures other than the reported Tc values would show that the superconductivity does not originate from the primary alloy phase.

read the original abstract

Since the first report of a high entropy alloy (HEA) superconductor in 2014, HEAs have continued to captivate the interest of superconducting researchers. Owing to the significant degree of disorder inherent in these systems, they serve as exemplary models for examining the properties of materials that exist in states intermediate between crystalline and amorphous structures. Here we present the superconductivity properties and crystal structure of TaNbHfZrAl and TiHfNbTaAl HEAs, which both have the VEC of 4.2 and body centered cubic (BCC) structure. Through resistivity, magnetic, and specific heat measurements, we prove that both samples are the bulk type-II superconductors with a critical temperature Tc of 5.5 K for TaNbHfZrAl and Tc of 3.2 K for TiHfNbTaAl. The Tc of HEA superconductors is influenced by the VEC and the element composition. And the incorporation of Al in high disorder HEA superconductors causes a more crystallinelike Tc dependence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports the synthesis and characterization of two Al-containing high-entropy alloys, TaNbHfZrAl and TiHfNbTaAl, both with valence electron count (VEC) of 4.2 and body-centered cubic (BCC) structure. Using resistivity, magnetic susceptibility, and specific-heat measurements, the authors claim to establish that both compounds exhibit bulk type-II superconductivity, with Tc = 5.5 K for TaNbHfZrAl and Tc = 3.2 K for TiHfNbTaAl. The work further discusses how VEC and Al incorporation influence Tc in disordered HEA systems, suggesting a more crystalline-like dependence.

Significance. If the bulk-superconductivity assignment is robustly supported, the results add two new examples to the catalog of HEA superconductors and illustrate how Al substitution can modulate the Tc(VEC) relation in highly disordered alloys, potentially clarifying the crossover between crystalline and amorphous limits.

major comments (2)
  1. [Abstract] Abstract: The assertion that resistivity, magnetic, and specific-heat data 'prove' bulk superconductivity in the majority BCC phase is not accompanied by the quantitative checks required to exclude minority-phase or surface contributions (e.g., Meissner volume fraction, normalized jump ΔC/γTc versus the BCS value 1.43, or upper limits on secondary phases from diffraction).
  2. [Crystal structure / Results] Crystal-structure section: The claim of a single BCC phase with VEC = 4.2 is stated without reported Rietveld refinement statistics or quantitative phase-purity limits, leaving open the possibility that the observed transitions arise from a minority phase whose volume fraction is not constrained by the presented data.
minor comments (1)
  1. [Abstract] Abstract: The phrasing 'the incorporation of Al in high disorder HEA superconductors causes a more crystallinelike Tc dependence' would benefit from an explicit comparison to the Tc(VEC) trend reported in prior HEA literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments correctly identify areas where additional quantitative analysis and clearer reporting would strengthen the manuscript. We will revise the paper to incorporate the suggested checks and metrics while preserving the core claims, which are supported by the existing data.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that resistivity, magnetic, and specific-heat data 'prove' bulk superconductivity in the majority BCC phase is not accompanied by the quantitative checks required to exclude minority-phase or surface contributions (e.g., Meissner volume fraction, normalized jump ΔC/γTc versus the BCS value 1.43, or upper limits on secondary phases from diffraction).

    Authors: We agree that the abstract's phrasing is strong and that explicit quantitative metrics improve rigor. In the revised manuscript we will report the Meissner volume fraction extracted from the zero-field-cooled susceptibility, compute and quote the normalized specific-heat jump ΔC/γTc (which lies near the BCS value), and provide upper limits on secondary phases from the XRD patterns. The abstract language will be moderated to 'establish' rather than 'prove' and will reference these new quantitative checks. revision: yes

  2. Referee: [Crystal structure / Results] Crystal-structure section: The claim of a single BCC phase with VEC = 4.2 is stated without reported Rietveld refinement statistics or quantitative phase-purity limits, leaving open the possibility that the observed transitions arise from a minority phase whose volume fraction is not constrained by the presented data.

    Authors: The XRD data indicate a single BCC phase, but we accept that Rietveld statistics and explicit purity limits are needed. In revision we will add Rietveld refinement results (including goodness-of-fit parameters) and quantitative upper bounds on any undetected impurity phases (estimated < 2 % from peak-search analysis). This will directly constrain the volume fraction of any minority phase that could contribute to the observed transitions. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental report with no derivations or fits

full rationale

The manuscript is an experimental characterization paper. It reports measured resistivity, magnetization, and specific-heat data on two HEA samples, states the observed Tc values, and notes the BCC structure and VEC=4.2. No equations, parameter fits, predictive models, or self-citation chains appear in the provided text. The central claim is therefore a direct reporting of observations rather than a derivation that could reduce to its inputs by construction. This is the normal non-circular outcome for a measurement-only study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard interpretations of transport, magnetic, and calorimetric signatures as evidence of bulk superconductivity; no new free parameters, axioms beyond domain conventions, or invented entities are introduced.

axioms (1)
  • domain assumption A sharp drop in resistivity to zero, diamagnetic response, and specific-heat jump together indicate a bulk superconducting transition.
    Invoked when the abstract states that the three measurements prove bulk superconductivity.

pith-pipeline@v0.9.1-grok · 5744 in / 1168 out tokens · 28232 ms · 2026-06-29T23:48:13.893627+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

43 extracted references

  1. [1]

    George E P, Raabe D and Ritchie R O 2019 High-entropy alloys Nat. Rev. Mater. 4 515- 34

    2019

  2. [2]

    Zeng L, Li L , Li K, Chen R and Luo H 2024 Recent advances in high -entropy superconductors NPG Asia Mater. 16 60

    2024

  3. [3]

    Sun L , Cava R J 2019 High-entropy alloy superconductors: Status, opportunities, and challenges Phys. Rev. Mater. 3 090301

    2019

  4. [4]

    Zhang D, Hsu Y C, Dunand D C 2024 Ink-Extrusion 3D Printing and Silicide Coating of HfNbTaTiZr Refractory High-Entropy Alloy for Extreme Temperature Applications Adv. Sci. 11 2309693

    2024

  5. [5]

    Rao Z et al 2021 Beyond Solid Solution High -Entropy Alloys: Tailoring Magnetic Properties via Spinodal Decomposition Adv. Funct. Mater. 31 2007668

    2021

  6. [6]

    Jung S G et al 2022 High critical current density and high-tolerance superconductivity in high-entropy alloy thin films Nat. Commun. 13 3373

    2022

  7. [7]

    Zeng L et al 2023 Discovery of the High -Entropy Carbide Ceramic Topological Superconductor Candidate (Ti0.2Zr0.2Nb0.2Hf0.2Ta0.2)C Adv. Funct. Mater. 33 2301929

    2023

  8. [8]

    Zeng L, Wang J, Liu H, Li L, Qin J, Li Y, Chen R, Song J, Hou Y and Luo H 2025 Ambient- Pressure Superconductivity Onset at 10 K and Robust Tc under High Pressure in TiNbTaN3 Medium-Entropy Nitride Adv. Sci. 12 e06089

    2025

  9. [9]

    Koželj P, Vrtnik S, Jelen A, Jazbec S, Jagličić Z, Maiti S, Feuerbacher M, Steurer W and Dolinšek J 2014 Discovery of a Superconducting High-Entropy Alloy Phys. Rev. Lett. 113 107001

    2014

  10. [10]

    Natl Acad

    Guo J et al 2017 Robust zero resistance in a superconducting high -entropy alloy at pressures up to 190 GPa Proc. Natl Acad. Sci. USA 114 13144-7

    2017

  11. [11]

    Zeng L et al 2024 Superconductivity in the High -Entropy Ceramics Ti0.2Zr0.2Nb0.2Mo0.2Ta0.2Cx with Possible Nontrivial Band Topology Adv. Sci. 11 2305054

    2024

  12. [12]

    Jangid S, Meena P K, Kushwaha R K, Srivastava S, Manna P, Mishra P, Sharma S and Singh R P 2024 Superconductivity with a high upper critical field in an equiatomic high- entropy alloy Sc–V–Ti–Hf–Nb Appl. Phys. Lett. 124 192602

    2024

  13. [13]

    223 115099

    Xiao G, Yang W, Zhu Q, Song S, Cao G H and Ren Z 2023 Superconductivity with large upper critical field in noncentrosymmetric Cr-bearing high-entropy alloys Scripta Mater. 223 115099

    2023

  14. [14]

    Li L et al 2025 Large upper critical fields and strong coupling s uperconductivity in the medium-entropy alloy (Ti1/3Hf1/3Ta1/3)1−xNbx Supercond. Sci. Technol. 38 015025

    2025

  15. [15]

    232 117971

    Kim J H , Hidayati R, Jung S G, Salawu Y A, Kim H J, Yun J H and Rhyee J S 2022 Enhancement of critical current density and strong vortex pinning in high entropy alloy superconductor Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 synthesized by spark plasma sintering Acta Mater. 232 117971

    2022

  16. [16]

    186 250-6

    Kim G, Lee M H, Yun J H, Rawat P, Jung S G, Choi W, You T S, Kim S J and Rhyee J S 2020 Strongly correlated and strongly coupled s-wave superconductivity of the high entropy alloy Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 compound Acta Mater. 186 250-6

    2020

  17. [17]

    China Phys

    Zeng L et al 2023 Extremely strong coupling s-wave superconductivity in the medium- entropy alloy TiHfNbTa Sci. China Phys. Mech. Astron. 66 277412

    2023

  18. [18]

    Huang Z et al 2025 Strong correlation behavior and strong coupling superconductivity in (Ti1/4Hf1/4Nb1/4Ta1/4)1−xNix with the rich magnetic element Ni Supercond. Sci. Technol. 38 085017

    2025

  19. [19]

    Zeng L et al 2023 Superconductivity and non -trivial band topology in high -entropy carbonitride Ti0.2Nb0.2Ta0.2Mo0.2W0.2C1-xNx Innov. Mater. 1 100042

    2023

  20. [20]

    Zeng L et al 2023 Superconductivity in the bcc-Type High-Entropy Alloy TiHfNbTaMo Adv. Quantum. Technol. 6 2300213

    2023

  21. [21]

    Wu L et al 2024 Record-High Tc and Dome -Shaped Superconductivity in a Medium - Entropy Alloy TaNbHfZr under Pressure up to 160 GPa Phys. Rev. Lett. 132 166002

    2024

  22. [22]

    Liu Y, Chen M, Li Y and Chen X 2009 Microstructure and Mechanical Performance of AlxCoCrCuFeNi High-Entropy Alloys Rare Metal Mat. Eng. 38 1602-7

    2009

  23. [23]

    Sun X, Zhang H, Li W, Ding X, Wang Y and Vitos L 2020 Generalized Stacking Fault Energy of Al-Doped CrMnFeCoNi High-Entropy Alloy Nanomaterials 10 59

    2020

  24. [24]

    Bean C P 1964 Magnetization of High-Field Superconductors Rev. Mod. Phys. 36 31-39

    1964

  25. [25]

    Yamafuji K, Fujiyoshi T, Toko K, Matsuno T, Kobayashi T and Kishio K 1994 On the magnetic field dependence of critical current density in single crystals of high -Tc superconductors Physica C 226 133-42

    1994

  26. [26]

    Matsumoto K, Takewaki H, Tanaka Y, Miura O, Yamafuji K, Funaki K, Iwakuma M and Matsushita T 1994 Enhanced J c properties in superconducting NbTi composites by introducing Nb artificial pins with a layered structure Appl. Phys. Lett. 64 115-7

    1994

  27. [27]

    Nature 399 439-42

    Dam B et al 1999 Origin of high critical currents in YBa 2Cu3O7−δ superconducting thin films. Nature 399 439-42

    1999

  28. [28]

    Rodriguez J P and Maley M P 2006 Collective pinning of imperfect vortex lattices by material line defects in extreme type-II superconductors Phys. Rev. B 73 094502

    2006

  29. [29]

    Jung S G, Vanacken J, Moshchalkov V V, Renosto S T, dos Santos C A M, Machado A J S, Fisk Z and Albino Aguiar J 2013 Critical current density and flux pinning in Zr0.96V0.04B2 superconductor with AlB2 structure J. Appl. Phys. 114 133905

    2013

  30. [30]

    Dew-Hughes D 1974 Flux pinning mechanisms in type II superconductors Philos. Mag. 30 293-305

    1974

  31. [31]

    Larbalestier D C et al 2001 Strongly linked current flow in polycrystalline forms of the superconductor MgB2 Nature 410 186-9

    2001

  32. [32]

    Shi Z, Wang J, Lv H and Tamegai T 2006 Effect of anisotropic superconductivity on flux pinning in polycrystalline MgB2 Physica C 449 104-8

    2006

  33. [33]

    Wang J, Shi Z X, Lv H and Tamegai T 2006 Effect of two-gap structure on flux pinning in MgB2 Physica C 445 462-5

    2006

  34. [34]

    Tripathi D and Dey T K 2013 A new scaling relation for n -AlN doped superconducting MgB2 J. Appl. Phys. 114

    2013

  35. [35]

    Gui X and Cava R J 2022 LaIr3Ga2: A Superconductor Based on a Kagome Lattice of Ir Chem. Mater. 34 2824-32

    2022

  36. [36]

    Górnicka K, Gui X, Wiendlocha B, Nguyen L T, Xie W, Cava R J and Klimczuk T 2021 NbIr2B2 and TaIr2B2 – New Low Symmetry Noncentrosymmetric Superconductors with Strong Spin–Orbit Coupling. Adv. Funct. Mater. 31 2007960

    2021

  37. [37]

    Johnston D C 2013 Elaboration of the α-model derived from the BCS theory of superconductivity Supercond. Sci. Technol. 26 115011

    2013

  38. [38]

    Kushwaha R K et al 2024 Unconventional properties of the noncentrosymmetric superconductor Re8NbTa Phys. Rev. B 109, 174518

    2024

  39. [39]

    Krishnan M et al 2025 Superconducting ground state and electronic properties of σ-Phase Ta–W–Mo-Re-Os high entropy alloys J. Phys. Chem. Solids 202, 112630

    2025

  40. [40]

    Jangid S, Meena P K, Kushwaha R K, Srivastava S, Manna P, Mishra P, Sharma S and Singh R P 2024 Superconductivity with a high upper critical field in an equiatomic high- entropy alloy Sc–V–Ti–Hf–Nb Appl. Phys. Lett. 124, 192602

    2024

  41. [41]

    Natl Acad Sci

    von Rohr F, Winiarski M J, Tao J, Klimczuk T and Cava R J 2016 Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor Proc. Natl Acad Sci. USA 113 E7144-E7150

    2016

  42. [42]

    Matthias B T 1955 Empirical Relation between Superconductivity and the Number of Valence Electrons per Atom Phys. Rev. 97 74-6

    1955

  43. [43]

    von Rohr F and Cava R J 2018 Isoelectronic substitutions and aluminium alloying in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor Phys. Rev. Mater. 2, 034801. Supporting Information Superconductivity in Al-based high-entropy alloys TiHfNbTaAl and TaNbHfZrAl Junjin Huanga,#, Wenbo Suna,#, Longfu Lia, Shuangyue Wanga, Jingjun Qina, Rui Chena, Zaichen ...

    2018