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Multiband Superconductivity and High Critical Current Density in Entropy Stabilized Nb0.25Ta0.25Ti0.25Zr0.25

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Pith's one-line read The paper argues that the entropy-stabilized alloy Nb0.25Ta0.25Ti0.25Zr0.25 is a bulk superconductor at 8 K with strong-coupling, likely multiband pairing, an upper critical field of about 11.94 T, and a critical current density above…

desk verdict Credible new HEA superconductor data with a record as-cast Jc, but the multiband and topological claims are overinterpreted from a single specific-heat exponent. read the letter →

arxiv 2508.19584 v1 pith:VZ63NASY submitted 2025-08-27 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Nikita Sharma , Kuldeep Kargeti , Neha Sharma , Pooja Chourasia , B. Vignolle , Olivier Toulemonde , Tirthankar Chakraborty , S. K. Panda
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Sourav Marik
This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-scicond-mat.str-el
keywords high-entropyalloysmedium-entropymultibandsuperconductivitystrong-couplingcriticalcurrentdensityupperfieldDirac-likebandcrossingsspecificheat
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that entropy-stabilized alloys, materials with several atomic species randomly mixed on one lattice, can host useful superconductivity rather than disorder suppressing pairing. It studies the equiatomic BCC alloy of niobium, tantalum, titanium, and zirconium and reports a bulk transition near 8 K, an upper critical field near 12 T, and a critical current density exceeding $10^{5}$ A/cm² in the as-cast state, which would surpass all previously reported as-cast high- and medium-entropy superconductors by orders of magnitude. On the microscopic side, the authors argue that a large specific-heat jump and a sublinear field dependence of the electronic specific-heat coefficient point to strong-coupling multiband superconductivity, while density-functional calculations show Dirac-like band crossings near the Fermi level, one of which survives spin-orbit coupling. If correct, the material would be a platform where severe intrinsic disorder, multiband pairing, and topological electronic states coexist, and a practical candidate for high-field superconducting applications.

What carries the argument

The argument is carried by three linked quantities. First, the electronic specific heat in the vortex state, reduced to the normalized Sommerfeld coefficient γ(H)/γn, gives a fitted power law $H^{0}$.55 that the paper treats as the experimental fingerprint of multiband pairing, because it lies between the linear behavior expected for single-gap vortex cores and the square-root behavior expected for nodal gaps. Second, the zero-field specific-heat jump and the electron-phonon coupling constants derived from Tc and the lattice vibrational temperature give the strong-coupling part, with ΔC/γTc ≈ 2.3 and coupling estimates in the range 0.86–1.39. Third, the DFT band structure supplies the topological suggestion: linear band crossings near the Fermi level, one surviving spin-orbit coupling, in a matrix where disorder would normally wash out such features. The pinning analysis, using a critical-state extraction of Jc and the $h^{0}$.5(1−h)^2 scaling of the pinning force, completes the practical case by attributing the high current density to grain-boundary surface pinning.

What would settle it

A gap-resolving experiment, such as point-contact Andreev reflection spectroscopy, scanning tunnelling spectroscopy, or a two-gap fit to the same specific-heat data, that finds only one superconducting gap would falsify the multiband claim; alternatively, a computed γ(H) from the band structure that reaches $H^{0}$.55 without multiple bands would show the interpretation is not unique.

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Extended reading notes

Core claim

The paper claims that the equiatomic BCC medium-entropy alloy Nb0.25Ta0.25Ti0.25Zr0.25 is a bulk, strong-coupling superconductor with Tc ≈ 8 K, an upper critical field Hc2(0) ≈ 11.94 T, and a critical current density Jc ≈ 1.3–1.4 × $10^{5}$ A/cm² in the as-cast state. It interprets the specific-heat jump ΔC/γTc ≈ 2.3, above the BCS weak-coupling value of 1.43, together with the sublinear field dependence γ(H)/γn ∝ (H/Hc2(0))^0.55 as evidence for multiband strong-coupling pairing, comparing that exponent with known multiband superconductors. Density-functional calculations on a special quasirandom structure show Dirac-like band crossings near the Fermi level, and one crossing between the A and Γ points remains degenerate when spin-orbit coupling is included; the paper reads this as a symmetry-protected topological feature coexisting with disorder and superconductivity. The high critical current is attributed to surface pinning at grain boundaries, with the normalized pinning force following $h^{0}$.5(1−h)^2, a surface-pinning form.

Load-bearing premise

The multiband conclusion depends on interpreting the measured γ(H) ∝ $H^{0}$.55 as a multiband fingerprint; if a single anisotropic gap or strong-coupling anisotropy can explain that sublinear field dependence, the paper's central claim loses its experimental support.

Editorial extensions

If this is right

  • A two-gap or multigap fitting procedure applied to the same specific-heat data would provide a quantitative check of the claimed multiband state.
  • Systematic annealing studies that tune grain size should either confirm or weaken the surface-pinning explanation for the high Jc.
  • If the 8 K transition and 11.94 T upper critical field hold in conductor form, this alloy becomes a disordered, irradiation-tolerant competitor to NbTi for high-field magnets.
  • Confirmation of the SOC-protected band crossing by angle-resolved photoemission would connect entropy-stabilized alloys to the study of topological superconductivity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that its γ(H) ∝ H^0.55 criterion is not unique to multiband pairing; a single anisotropic gap or strong-coupling anisotropy can also produce sublinear growth, so a two-gap fit or a phase-sensitive probe is the natural next experiment.
  • I infer that the topological claim should be stress-tested against disorder: the DFT calculation used one finite supercell, and checking several random configurations or a larger supercell would show whether the surviving degeneracy is a robust property of the alloy rather than of that particular cell.
  • A testable extension is thermomagnetic stability: the annealed sample shows flux jumps, so sweep-rate-dependent magnetization measurements could separate intrinsic disorder pinning from magnetothermal instabilities and guide annealing protocols toward higher Jc.
  • Because the as-cast Jc already approaches the practical 10^5 A/cm² benchmark with no optimization, conductor-level processing of this alloy is a plausible next step, though the paper does not address it.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports a combined experimental and computational study of the equiatomic bcc medium-entropy alloy Nb0.25Ta0.25Ti0.25Zr0.25. The authors show bulk superconductivity with Tc ≈ 8 K, an upper critical field Hc2(0) ≈ 11.94 T from resistivity in fields up to 10 T, a lower critical field Hc1(0) ≈ 68 mT, and a critical current density exceeding 10^5 A/cm² at low fields for the as-cast sample. Specific heat measurements reveal a jump ΔC/γTc ≈ 2.3 and a field-dependent Sommerfeld coefficient that scales as γ(H) ∝ H^0.55, which the authors interpret as evidence of multiband strong-coupling superconductivity. DFT-based SQS calculations show dynamical stability, a high d-electron DOS at the Fermi level, and several Dirac-like band crossings, some of which survive spin-orbit coupling. The paper claims this is the highest Tc among medium/high-entropy alloys and highlights possible unconventional and/or topological superconductivity together with high critical current density.

Significance. If the multiband and topological interpretations were firmly established, this would be an important advance: it would identify a new entropy-stabilized superconductor with Tc ≈ 8 K, a comparatively high Hc2, and record-high critical current density among as-cast high/medium-entropy alloys, while connecting severe intrinsic disorder with unconventional pairing. The experimental dataset is broad and internally consistent for the bulk superconducting parameters: transport, magnetization, and specific heat all point to Tc ≈ 8 K and Hc2(0) ≈ 12 T, and the as-cast low-field Jc value is credible. The DFT phonon stability and electronic structure calculations add value. However, the load-bearing claim of multiband superconductivity rests almost entirely on one phenomenological scaling law, γ(H) ∝ H^0.55, which is not a diagnostic, and the strong-coupling story is weakened by an internal inconsistency in the reported electron-phonon coupling constant. The paper's central physics claim therefore needs substantially more support or a more modest framing.

major comments (3)
  1. [Field-dependent specific heat, Figure 5(d)] The multiband conclusion is anchored on the observation that γ(H)/γn scales as (H/Hc2)^0.55, interpreted by analogy with MgB2, LaNiC2, FeSe, and Re24Nb5. This is not a sufficient diagnostic. A sublinear γ(H) also follows from nodal or strongly anisotropic single-gap superconductors via the Volovik √H effect, and the paper itself plots the nodal-gap curve in Figure 5(d). The low-temperature fit in Eq. (16) describes a nodeless exponential gap, consistent with a single-gap BCS-like superconductor, and the α-model fit in Figure 5(b) is a single-gap fit; neither independently supports multiple bands. To justify the multiband label, the authors should provide a two-gap fit to C(T,H), a computed γ(H) from the DFT Fermi surface, or an independent probe of multiple gaps (e.g., penetration depth or muon spin rotation). As written, the headline claim of multiband superconductivity is not secured.
  2. [Critical current density, annealed sample] In the paragraph describing the annealed sample, the Jc values that exceed 10^5 A/cm² up to 5 T are estimated from 'the surface points of the MH loops' of loops that exhibit flux jumps. This method is not described. The Bean model, Eq. (11), normally uses the full width ΔM of a complete hysteresis loop; using selected 'surface points' without defining a selection procedure makes the annealed-sample Jc values unverifiable and potentially dependent on arbitrary choices. Please specify exactly how the surface points were chosen, how flux jumps were handled, and whether the Bean formula remains applicable to partial loops. The as-cast Jc values below 0.25 T appear credible, but the annealed high-field claim needs proper documentation before it can be used to support the benchmark-exceeding Jc claim.
  3. [Table II and strong-coupling analysis] There is an internal inconsistency in the electron-phonon coupling constant. Table II lists λe-ph = 0.86 ± 0.02, matching the McMillan value obtained from Eq. (15), but the text immediately after Eq. (19) states that the Allen-Dynes equation gives λe-ph = 1.39. Both values are used to support strong coupling, but they differ by more than 60%. The authors should explain which value is the final estimate, why the two formulas differ so strongly, and what λe-ph is used in subsequent statements (e.g., the density-of-states estimate in Eq. (14)). This discrepancy directly affects the strong-coupling characterization that is part of the paper's central interpretation.
minor comments (4)
  1. [WHH fit (Figure 3(c))] The text reports λSO = 1.63 from the WHH fit, while the caption of Figure 3(c) states λSO = 1.62; please use a consistent value.
  2. [α-model and Eq. (18)] Figure 5(b) gives Δ(0)/kBTc = 1.9 from the α-model fit, while Eq. (18) yields Δ(0)/kBTc ≈ 2.09; the text says these 'closely match,' but the 10% difference should at least be acknowledged or explained.
  3. [Eq. (5)] The Ginzburg-Landau expression for Hc2(T) in Eq. (5) is not a standard form; please justify it or reference the specific model used, since the extracted Hc2(0) depends on this choice.
  4. [General editing] There are several typographical issues, including 'residual residual resistivity' in the text near Eq. (1), and the repeated use of 'highlight the possibility' phrasing in the abstract and conclusions, which could be tightened.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's headline quantities are direct measurements, and the multiband and strong-coupling interpretations are analogies and consistency checks rather than derivations that reduce to their own inputs.

full rationale

The paper's central measured quantities — Tc ≈ 8 K, Hc2(0) ≈ 11.94 T, ΔC/γTc ≈ 2.3, and Jc > 10^5 A/cm² — are direct observations, not outputs of a fitted model. The multiband claim rests on the observed sublinear field dependence γ(H) ∝ H^0.55, which is compared by analogy with known multiband superconductors; no two-gap fit or band-structure-derived γ(H) is provided, so the interpretation is under-supported but not circular. The strong-coupling parameters (ωln, 2Δ/kBTc, and λe-ph from the Allen-Dynes equation) are computed from the measured specific-heat jump using standard strong-coupling formulas (Eqs. 17–19); these are consistency checks, not independent predictions, and they do not redefine the measured jump. The DFT band-structure and phonon calculations are independent ab initio inputs. The self-citations in the VEC–Tc comparison (Fig. 6(b)) are only data compilation and are not load-bearing for the paper's claims. The internal inconsistency between λe-ph = 0.86 (Table II, McMillan formula) and λe-ph = 1.39 (Allen-Dynes estimate in the text) is a correctness concern, as is the insufficient diagnostic power of the γ(H) exponent for multiband superconductivity, but neither constitutes circularity under the required standard.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central experimental facts rest on standard characterization models and the SQS-based DFT approximation. The load-bearing assumptions are the interpretive mapping from the γ(H) power law to multiband pairing, and the non-standard Jc extraction for the annealed sample; both are explicit in the text and are not independently corroborated.

free parameters (4)
  • lambda_SO (spin-orbit scattering parameter) = 1.62 (also given as 1.63 in text)
    Fitted in the one-band WHH model to match the measured Hc2(T) curve; used to attribute the upper critical field enhancement to spin-orbit scattering.
  • alpha_M (Maki parameter) = 1.17
    Fitted in the WHH analysis (earlier estimated as ≃1 from Eq. 9); adjusts the relative strength of orbital and Pauli limiting.
  • Delta(0)/k_B Tc (alpha-model gap ratio) = 1.9
    Fitted to the electronic specific heat jump using the α model; characterizes the gap but is not an independent prediction.
  • n (field-dependence exponent of gamma) = 0.55
    Power-law fit of gamma(H)/gamma_n versus H/Hc2; this exponent is the principal experimental evidence for multiband superconductivity.
assumptions (5)
  • domain assumption Bean's critical state model applies to the bulk polycrystalline sample and the reported Jc follows from the M-H loop width.
    Used in Eq. 11 to compute Jc; assumes uniform bulk pinning and neglects surface screening and geometry effects.
  • domain assumption The normal-state specific heat is described by a single electronic γT plus one Debye phonon βT^3 term.
    Used to extract γ and β from C/T vs T^2; additional low-energy modes or a two-band phonon spectrum could bias these values.
  • domain assumption The SQS supercell used in DFT captures the electronic structure of the infinite random solid solution.
    The Dirac-like crossings in Figure 8 are computed for one finite SQS configuration; disorder may broaden or destroy these crossings, and no ensemble averaging over configurations is performed.
  • ad hoc to paper The sublinear field dependence gamma(H) ∝ H^0.55 is a signature of multiband superconductivity.
    The paper compares with other multiband superconductors but does not rule out nodal gaps, strong coupling, or single anisotropic gaps as alternative explanations.
  • ad hoc to paper For the annealed sample, Jc can be estimated from the 'surface points' of M-H loops that exhibit flux jumps.
    The standard Bean model requires the full reversible hysteresis width; the unspecified 'surface points' method is not validated and can overestimate Jc.

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Cite this review

Pith. "Pith review of Multiband Superconductivity and High Critical Current Density in Entropy Stabilized Nb0.25Ta0.25Ti0.25Zr0.25." pith.science (2026). https://pith.science/paper/VZ63NASY

@misc{pith2026250819584,
  author       = {Pith},
  title        = {Pith review of: Multiband Superconductivity and High Critical Current Density in Entropy Stabilized Nb0.25Ta0.25Ti0.25Zr0.25},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VZ63NASY}},
  note         = {Machine review of arXiv:2508.19584}
}
read the original abstract

High and medium-entropy superconductors with significant intrinsic disorder are a fascinating class of superconductors. Their combination of robust structural integrity, superior mechanical properties, and exceptional irradiation tolerance makes them promising candidates for use in advanced superconducting technologies. Herein, we present a comprehensive theoretical and experimental investigation on the superconductivity of equiatomic entropy-stabilized Nb0.25Ta0.25Ti0.25Zr0.25. The material shows bulk superconductivity (transition temperature = 8K) with a high upper critical field of 11.94T. Interestingly, both the electronic band structure and specific heat data point toward unconventional multiband superconductivity. Our ab initio calculations reveal Dirac-like band crossings close to the Fermi level, with certain degeneracies persisting even in the presence of spin-orbit coupling, suggesting a possible interplay between topological electronic states and the observed unconventional superconductivity. Remarkably, the critical current density exceeds the benchmark of 10^5 A/cm2, surpassing all previously reported as-cast entropy-stabilized superconductors. This high critical current density is likely attributed to strong flux pinning at the grain boundaries, facilitated by extreme intrinsic lattice distortion. Taken together, the demonstrated dynamical stability, excellent metallicity, potential to host unconventional superconductivity, and exceptionally high critical current density highlight the potential of entropy-stabilized alloys as a platform for exploring the confluence of disorder, topology, and unconventional superconductivity.

Figures

Figures reproduced from arXiv: 2508.19584 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The room temperature powder X-ray diffraction pattern (red sphere) and Rietveld refinement (black line) of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The temperature-dependent dc-electrical resistivity (H = 1 mT) along with the Bloch-Gruneisen (BG) and power law [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The observed lower critical field as a function of reduced temperature. Inset shows the field-dependent magnetiza [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a)Magnetic hysterisis loop (M-H) at temperatures ranging from 2 K to 4 K for Nb [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) C/T vs T [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Vortex phase diagram of Nb [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Calculated phonon dispersion of Nb [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Band dispersion of Nb [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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Works this paper leans on

76 extracted references · 64 canonical work pages

  1. [1]

    Boutboul, S

    T. Boutboul, S. Le Naour, D. Leroy, L. Oberli, and V. Previtali, IEEE Transactions on Applied Superconduc- tivity 16, 1184 (2006)

    work page 2006

  2. [2]

    Banno, Superconductivity 6, 100047 (2023)

    N. Banno, Superconductivity 6, 100047 (2023)

    work page 2023

  3. [3]

    L. Zeng, J. Wang, H. Liu, L. Li, J. Qin, Y. Li, R. Chen, J. Song, Y. Hou, and H. Luo, Advanced Science , e06089 (2025)

    work page 2025

  4. [4]

    L. Zeng, Z. Wang, J. Song, G. Lin, R. Guo, S. C. Luo, S. Guo, K. Li, P. Yu, C. Zhang, W. M. Guo, J. Ma, Y. Hou, and H. Luo, Advanced Functional Materials 33, 2301929 (2023)

    work page 2023

  5. [5]

    Koželj, S

    P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličič, S. Maiti, M. Feuerbacher, W. Steurer, and J. Dolinšek, Physical Review Letters 113, 107001 (2014)

    work page 2014

  6. [6]

    J. Guo, H. Wang, F. von Rohr, Z. Wang, S. Cai, Y. Zhou, K. Yang, A. Li, S. Jiang, Q. Wu, R. J. Cava, and L. Sun, Proceedings of the National Academy of Sciences of the United States of America 114, 13144 (2017)

    work page 2017

  7. [7]

    Huang, J

    C. Huang, J. Guo, J. Zhang, K. Stolze, S. Cai, K. Liu, H. Weng, Z. Lu, Q. Wu, T. Xiang, R. J. Cava, and L. Sun, Physical Review Materials 4, 071801 (2020)

    work page 2020

  8. [8]

    Y. F. Ye, Q. Wang, J. Lu, C. Liu, and Y. Yang, Materials Today 19, 349 (2016)

    work page 2016

Show all 76 references
  1. [9]

    Gludovatz, A

    B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E.P.George, andR.O.Ritchie, Science345, 1153(2014)

    2014

  2. [10]

    D. H. Cook, P. Kumar, M. I. Payne, C. H. Belcher, P. Borges, W.Wang, F.Walsh, Z.Li, A.Devaraj, M.Zhang, A. Mark, A. M. Minor, E. J. Lavernia, D. Apelian, and R. O. Ritchie, Science 384, 178 (2024)

    2024

  3. [11]

    C. P. Lee, Y. Y. Chen, C. Y. Hsu, J. W. Yeh, and H. C. Shih, Journal of The Electrochemical Society 154, C424 (2007)

    2007

  4. [12]

    S. Jung, Y. Han, J. H. Kim, R. Hidayati, J. Rhyee, J. M. Lee, W. N. Kang, W. S. Choi, H. Jeon, J. Suk, and T. Park, Nature Communications 13, 3373 (2022)

    2022

  5. [13]

    B. Liu, J. Wu, Y. Cui, Q. Zhu, G. Xiao, S. Wu, G. Cao, and Z. Ren, Scripta Materialia 182, 109 (2020)

    2020

  6. [14]

    Stolze, J

    K. Stolze, J. Tao, F. O. Von Rohr, T. Kong, and R. J. Cava, Chemistry of Materials 30, 906 (2018)

    2018

  7. [15]

    A.Yamashita, T.D.Matsuda, andY.Mizuguchi, Journal of Alloys and Compounds 868, 159233 (2021)

    2021

  8. [16]

    Hirai, N

    D. Hirai, N. Uematsu, Y. Muramatsu, K. Deguchi, Y. Shimura, T. Onimaru, and K. Takenaka, Chemistry of Materials 36, 9547 (2024)

    2024

  9. [17]

    Van De Walle, M

    A. Van De Walle, M. Asta, and G. Ceder, Calphad 26, 539 (2002)

    2002

  10. [18]

    Van De Walle, Calphad 33, 266 (2009)

    A. Van De Walle, Calphad 33, 266 (2009)

    2009

  11. [19]

    van de Walle, P

    A. van de Walle, P. Tiwary, M. de Jong, D. L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L. Q. Chen, and Z. K. Liu, Calphad 42, 13 (2013)

    2013

  12. [20]

    Kresse and J

    G. Kresse and J. Hafner, Physical Review B 47, 558 (1993)

    1993

  13. [21]

    Kresse and J

    G. Kresse and J. Furthmüller, Computational Materials Science 6, 15 (1996)

    1996

  14. [22]

    Kresse and J

    G. Kresse and J. Furthmüller, Physical Review B 54, 11169 (1996)

    1996

  15. [23]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Physical Re- view Letters 77, 3865 (1996)

    1996

  16. [24]

    Senkov, J

    O. Senkov, J. Scott, S. Senkova, D. Miracle, and C. Woodward, Journal of Alloys and Compounds 509, 6043 (2011)

    2011

  17. [25]

    Supplemental Information

  18. [26]

    Motla, Arushi, S

    K. Motla, Arushi, S. Jangid, P. K. Meena, R. K. Kush- waha, andR.P.Singh, SuperconductorScienceandTech- nology 36, 115024 (2023)

    2023

  19. [27]

    Jangid, P

    S. Jangid, P. K. Meena, R. K. Kushwaha, S. Srivastava, P. Manna, P. Mishra, S. Sharma, and R. P. Singh, Ap- plied Physics Letters 124, 192602 (2024)

    2024

  20. [28]

    Grimvall, Physica Scripta 14, 63 (1976)

    G. Grimvall, Physica Scripta 14, 63 (1976)

    1976

  21. [29]

    N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Physical Review 147, 295 (1966)

    1966

  22. [30]

    D.Yan, D.Geng, Q.Gao, Z.Cui, C.Yi, Y.Feng, C.Song, H. Luo, M. Yang, M. Arita, S. Kumar, E. F. Schwier, K. Shimada, L. Zhao, K. Wu, H. Weng, L. Chen, X. J. Zhou, Z. Wang, Y. Shi, and B. Feng, Physical Review B 102, 205117 (2020)

    2020

  23. [31]

    Tinkham, Introduction to Superconductivity, 2nd ed

    M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York, NY, 1996)

    1996

  24. [32]

    Klimczuk, F

    T. Klimczuk, F. Ronning, V. Sidorov, R. J. Cava, and J. D. Thompson, Physical Review Letters 99, 257004 (2007)

    2007

  25. [33]

    Maki, Physics Physique Fizika 1, 127 (1964)

    K. Maki, Physics Physique Fizika 1, 127 (1964)

    1964

  26. [34]

    Maki, Physical Review 148, 362 (1966)

    K. Maki, Physical Review 148, 362 (1966)

    1966

  27. [35]

    H. Liu, J. Yao, J. Shi, Z. Yang, D. Yan, Y. Li, D. Chen, H. L. Feng, S. Li, Z. Wang, and Y. Shi, Physical Review B 108, 104504 (2023)

    2023

  28. [36]

    C. P. Bean, Reviews of Modern Physics 36, 31 (1964)

    1964

  29. [37]

    Hidayati, J

    R. Hidayati, J. H. Kim, S. G. Jung, K. S. Cho, J. H. Yun, and J. S. Rhyee, Acta Materialia 261, 119420 (2023). 13

    2023

  30. [38]

    G. Kim, M. H. Lee, J. H. Yun, P. Rawat, S. G. Jung, W. Choi, T. S. You, S. J. Kim, and J. S. Rhyee, Acta Materialia 186, 250 (2020)

    2020

  31. [39]

    B. Dam, J. Huijbregtse, F. Klaassen, R. Van Der Geest, G. Doornbos, J. Rector, A. Testa, S. Frelsem, J. Mar- tinez, B. Stauble-Pumpin, and R. Griessen, Nature 399, 439 (1999)

    1999

  32. [40]

    Civale, B

    L. Civale, B. Maiorov, A. Serquis, J. Willis, J. Coulter, H. Wang, Q. Jia, P. Arendt, J. MacManus-Driscoll, M. Maley, and S. Foltyn, Applied Physics Letters 84, 2121 (2004)

    2004

  33. [41]

    Dew-Hughes, Philosophical Magazine 30, 293 (1974)

    D. Dew-Hughes, Philosophical Magazine 30, 293 (1974)

    1974

  34. [42]

    D. C. Larbalestier, in Superconductor Materials Science: Metallurgy, Fabrication, and Applications (Springer,

  35. [43]

    Meingast, P

    C. Meingast, P. Lee, and D. Larbalestier, Journal of Ap- plied Physics 66, 5962 (1989)

    1989

  36. [44]

    W. L. McMillan, Physical Review 167, 331 (1968)

    1968

  37. [45]

    Elrod, J

    S. Elrod, J. Miller, and L. Dresner, in Advances in Cryo- genic Engineering Materials (1981) pp. 601–610

    1981

  38. [46]

    A. T. Hirshfeld, H. Leupold, and H. Boorse, Physical Review 127, 1501 (1962)

    1962

  39. [47]

    Cucciari, D

    A. Cucciari, D. Naddeo, S. Di Cataldo, and L. Boeri, Physical Review B 110, L140502 (2024)

    2024

  40. [48]

    Kittel, Introduction to Solid State Physics, 8th ed

    C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, Hoboken, NJ, 2005)

    2005

  41. [49]

    B. T. Matthias, Physical Review 97, 74 (1955)

    1955

  42. [50]

    M. M. Collver and R. H. Hammond, Physical Review Letters 30, 92–95 (1973)

    1973

  43. [51]

    Marik, K

    S. Marik, K. Motla, M. Varghese, K. P. Sajilesh, D. Singh, Y. Breard, P. Boullay, and R. P. Singh, Physi- cal Review Materials 3, 060602(R) (2019)

    2019

  44. [52]

    F. O. V. Rohr, M. J. Winiarski, J. Tao, T. Klimczuk, and R. J. Cava, Proceedings of the National Academy of Sciences of the United States of America 113, E7144 (2016)

    2016

  45. [53]

    Sharma, N

    N. Sharma, N. Sharma, T. Chakraborty, and S. Marik, Materials Today Communications 44, 111968 (2025)

    2025

  46. [54]

    Sharma, J

    N. Sharma, J. Link, K. Kargeti, N. Sharma, I. Heinmaa, S. K. Panda, R. Stern, T. Chakraborty, T. Chakrabarty, and S. Marik, Physical Review Materials 9, 064801 (2025)

    2025

  47. [55]

    Padamsee, J

    H. Padamsee, J. Neighbor, and C. Shiffman, Journal of Low Temperature Physics 12, 387 (1973)

    1973

  48. [56]

    D. C. Johnston, Superconductor Science and Technology 26, 115011 (2013)

    2013

  49. [57]

    C.Caroli, P.DeGennes, andJ.Matricon, PhysicsLetters 9, 307 (1964)

    1964

  50. [58]

    Volovik, JETP Letters 58, 469 (1993)

    G. Volovik, JETP Letters 58, 469 (1993)

    1993

  51. [59]

    Volovik, JETP Letters 58, 444 (1993)

    G. Volovik, JETP Letters 58, 444 (1993)

    1993

  52. [60]

    Bouquet, R

    F. Bouquet, R. Fisher, N. Phillips, D. Hinks, and J. Jor- gensen, Physical Review Letters 87, 047001 (2001)

    2001

  53. [61]

    J. Chen, L. Jiao, J. L. Zhang, Y. Chen, L. Yang, M. Nicklas, F. Steglich, and H. Q. Yuan, New Journal of Physics 15, 053005 (2013)

    2013

  54. [62]

    J. Chen, Y. Sun, T. Yamada, S. Pyon, and T. Tamegai, in Journal of Physics: Conference Series, Vol. 871 (IOP Publishing, 2017) p. 012016

    2017

  55. [63]

    1 + 53 TC ωln 2 ln ωln 3TC # (17) With the obtained value ofωln = 80.7 K, the value of superconducting gap, can also be obtained through the following equation 2∆(0) kB TC = 3.53

    Nodal gap [58, 59] Nb 0.25 Ti 0.25 Ta 0.25 Zr 0.25 H [57] MgB 2 [60] 20151050Cel /T 7654321 T (K) 0T 0.5T 1T 1.5T 4T 5T 6T 7T 8T C el /T = γ + A/T exp(-bT c /T) 2T 2.5T 3T 3.5T (a) (d)(c) (b) FIG. 5. (a) C/T vs T2 in zero field for Nb0.25Ta0.25Ti0.25Zr0.25, fitted using Debye ...

  56. [64]

    Shang, M

    T. Shang, M. Smidman, S. K. Ghosh, C. Baines, L. J. Chang, D. J. Gawryluk, J. A. T. Barker, R. P. Singh, D. M. Paul, G. Balakrishnan, E. Pomjakushina, M. Shi, M. Medarde, A. D. Hillier, H. Q. Yuan, J. Quintanilla, J. Mesot, and T. Shiroka, Physical Review Letters 121, 257002 (2018)

    2018

  57. [65]

    M. P. Fisher, Physical Review Letters 62, 1415 (1989)

    1989

  58. [66]

    Chakrabortty and N

    S. Chakrabortty and N. Mohapatra, Physical Review B 111, 094511 (2025)

    2025

  59. [67]

    S. M. Young, S. Zaheer, J. C. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Physical review letters 108, 140405 (2012)

    2012

  60. [68]

    Z. Liu, B. Zhou, Y. Zhang, Z. Wang, H. Weng, D. Prab- hakaran, S. K. Mo, Z. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. Chen, Science 343, 864 (2014)

    2014

  61. [69]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Reviews of Modern Physics 90, 015001 (2018)

    2018

  62. [70]

    Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X.Dai, andZ.Fang, PhysicalReviewB85, 195320 (2012)

    2012

  63. [71]

    S. Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C. C. Lee, S. M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Science 349, 613 (2015)

    2015

  64. [72]

    B. J. Yang and N. Nagaosa, Nature communications 5, 4898 (2014)

    2014

  65. [73]

    Bradlyn, J

    B. Bradlyn, J. Cano, Z. Wang, M. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science 353, aaf5037 (2016)

    2016

  66. [74]

    F. K. Guo, C. Hanhart, U. G. Meißner, Q. Wang, Q. Zhao, and B. S. Zou, Reviews of Modern Physics 90, 015004 (2018)

    2018

  67. [75]

    B. J. Wieder, B. Bradlyn, Z. Wang, J. Cano, Y. Kim, H. S. D. Kim, A. M. Rappe, C. Kane, and B. A. Bernevig, Science 361, 246 (2018)

    2018

  68. [76]

    H. H. Hung, A. Barr, E. Prodan, and G. A. Fiete, Phys- ical Review B 94, 235132 (2016)

    2016

Pith tools

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