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Screening phonon-mediated superconductors from static orbital Hamiltonians

T0 review · 3 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A low-cost screening scheme estimates electron-phonon coupling directly from static orbital Hamiltonians, and applied to over 36,000 compounds it finds 34 dynamically stable superconducting candidates with calculated transition temperatures

desk verdict SEPR is a genuinely cheap and physically transparent EPC screening heuristic, but the universal decay length and threshold tuning make the candidate list a starting point, not a discovery. read the letter →

arxiv 2608.02426 v1 pith:2GFS7HPQ submitted 2026-08-03 cond-mat.supr-con

Jian-Feng Zhang , Ze-Feng Gao , Xiao-Qi Han , Dingshun Lv , Miao Gao , Kai Liu , Xinguo Ren , Zhong-Yi Lu
show 1 more author
Tao Xiang
This is my paper · ORCID
classification cond-mat.supr-con
keywords electron-phononcouplingsuperconductorscreeningstaticorbitalHamiltonianSEPRdensityfunctionalperturbationtheoryhigh-throughputmaterialsdiscoveryσ-bondmetallizationMcMillan-Allen-Dynes
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 claims that the electron-phonon coupling strength of a material can be estimated directly from its static orbital Hamiltonian, without computing phonon perturbations explicitly. It does this through three approximations—an averaged phonon frequency, bond-only hopping changes, and an exponential bond-length decay model—producing two screening quantities, Ξ and χ. Applied to 36,377 compounds, the scheme flags 260 candidates, of which 150 are dynamically stable and 34 have calculated Tc above 10 K after density functional perturbation theory verification. If correct, this makes high-throughput superconductor discovery much cheaper and reveals two physical routes to high Tc: metallized covalent σ-bonds and Fermi-level density-of-states accumulation.

What carries the argument

The central object is the static electron-phonon response (SEPR) scheme, which approximates the phonon-induced Hamiltonian derivative dH/du from static interatomic hopping integrals. Three approximations carry the argument: the dynamic isotropic approximation (mode-dependent phonon frequencies replaced by an average), the double-center approximation (only bonds directly attached to the displaced atom contribute), and the bonding-attractivity (BA) model (hopping integrals decay exponentially with bond length, with a uniform decay length L = 1.2 Å). These yield two screening quantities: Ξ, the mass-weighted EPC-related scattering scale, and χ, the mass-independent electronic deformation respon

What would settle it

Measure the superconducting transition of a predicted candidate that already has synthetic records, such as B13C2 (calculated Tc ≈ 41 K), at ambient pressure; if no superconductivity above 10 K is found, the screening ranking is called into question. Alternatively, compute DFPT Ξ for a series of 2p-covalent and alkali-based compounds and check whether the uniform-L SEPR values reproduce the ordering; large deviations would falsify the universal decay-length assumption.

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Extended reading notes

Core claim

The central claim is that the static electron-phonon response (SEPR) framework, built from static orbital Hamiltonians, reproduces the scale and material trends of electron-phonon coupling at a fraction of the cost of density functional perturbation theory. Using the mass-weighted scattering scale Ξ and the mass-independent deformation response χ, with thresholds Ξ > 15.0 meV and χ > 125.0 meV·u^1/2, the screen reduces 8,833 nonmagnetic metals to 260 candidates; subsequent DFPT phonon and EPC calculations yield 150 dynamically stable systems, 99 with Tc > 2 K, and 34 with Tc > 10 K. The paper interprets the survivors as showing two recurring routes to high Tc and a systematic competition bet

Load-bearing premise

The result rests on the assumption that every interatomic hopping integral decays exponentially with bond length with the same decay length L = 1.2 Å; if real decay lengths vary across chemical families (as the paper's own bias analysis suggests), the estimated Ξ and χ values—and hence the candidate list—are systematically skewed.

Editorial extensions

If this is right

  • EPC screening no longer requires explicit phonon perturbation at the initial stage, cutting evaluation time from hours to minutes.
  • The screen identifies 34 dynamically stable candidates with calculated Tc > 10 K, including known superconductors and previously untested boron/carbon-rich phases.
  • Two distinct routes to high Tc emerge: metallized covalent σ-bonds (larger per-state scattering V_ep) and Fermi-level DOS accumulation (larger N*(εF)).
  • The empty upper-right region of the V_ep–N*(εF) plane indicates a systematic competition between strong EPC and lattice stability, so optimal candidates should lie near the stability boundary.
  • Systematic bias analysis shows alkali/alkaline-earth systems tend to be overestimated and 2p-covalent systems underestimated, attributable to the uniform decay length.

Reading between the lines

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

  • If the uniform decay length were replaced by element-resolved decay lengths (e.g., about 0.8 Å for 2p elements and about 3.6 Å for alkali/alkaline-earth elements), the screening thresholds and candidate list could shift markedly; a quick test would be to recompute Ξ and χ with family-dependent L values.
  • The predicted dynamically unstable high-Ξ compounds, though excluded here, may become superconducting under pressure or with doping, exactly as the high-pressure hydrides did; this makes them a natural target for follow-up synthesis.
  • The SEPR decomposition into atom- and direction-resolved contributions could be used to identify the specific phonon modes that dominate coupling, potentially guiding isotope-substitution or strain experiments.
  • The same static-response logic could be paired with machine-learned or surrogate Hamiltonians to extend the screen far beyond the present 36,377-compound database, should such Hamiltonians become available.
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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 / 5 minor

Summary. The paper proposes a static electron-phonon response (SEPR) framework that estimates electron-phonon coupling (EPC) strength directly from static orbital-based Hamiltonians, bypassing DFPT at the screening stage. Three approximations are introduced: a dynamic isotropic average over phonon modes, a double-center approximation for hopping derivatives, and a bonding-attractivity (BA) model in which hopping integrals decay exponentially with bond length using a single universal decay length L = 1.2 Å. This yields two screening metrics, Ξ and χ. The method is benchmarked against DFPT for eight known superconductors (Table I), showing order-of-magnitude agreement at far lower computational cost. Applying thresholds Ξ > 15 meV and χ > 125 meV·u^{1/2} to 8,833 nonmagnetic metals in the MattKeyBond database gives 260 candidates; DFPT verification leaves 150 dynamically stable compounds, of which 99 have Tc > 2 K and 34 have Tc > 10 K. The paper further interprets the final candidates as following two routes to high-Tc superconductivity: metallized covalent σ-bonding and Fermi-level DOS accumulation.

Significance. If the central claims hold, SEPR would be a valuable low-cost, physically interpretable pre-filter for superconductor discovery in large chemical databases. The paper's strengths include the transparent decomposition of Ξ and χ into atom- and direction-resolved contributions, the DFPT benchmarks for eight systems at dramatically lower cost, and the open discussion of the method's systematic bias in Sec. V. The candidate list itself is DFPT-verified, so the 34 candidates are not mere artifacts of the screening metrics. However, the screening metrics rely on a single universal decay length and on absolute thresholds calibrated on known superconductors; the paper does not quantify how the documented family-dependent bias affects the final candidate list. This makes the 'semi-quantitative' cross-family claim currently under-supported, though the issue is addressable in revision.

major comments (3)
  1. [Sec. II C and Sec. V, Eq. (7)] The universal BA decay length L_A = 1.2 Å is load-bearing. Eq. (7) gives dH_ab/du ≈ -(R·e/|R|)/L · H_ab, so Ξ and χ scale approximately as 1/L. Sec. V and Fig. 4 report that alkali/alkaline-earth systems have effective L ≈ 3.6 Å and 2p-covalent systems L ≈ 0.8 Å. Thus SEPR overestimates the EPC response by about 3× for alkali-containing metals and underestimates it by about 1.5× for 2p-covalent metals. Because the thresholds Ξ > 15 meV and χ > 125 meV·u^{1/2} are absolute, this family bias directly changes the composition of the 260-compound pool and hence the 34 candidates. The paper acknowledges the bias but does not quantify its impact on the final list. Please provide a sensitivity analysis, e.g., re-running the screen with L = 0.8 Å and 3.6 Å or with element-dependent L, and state which candidates survive. Without this, the claim of a semi-quantitative EPC scale across broad chemica
  2. [Sec. IV, threshold selection] The criteria Ξ > 15.0 meV and χ > 125.0 meV·u^{1/2} are called 'benchmarked', but the benchmarking procedure is not reported. It is unclear whether these cutoffs were selected to include the known superconductors in Table I; if so, the screening success is partly in-sample. The absence of a threshold-sensitivity analysis makes it impossible to assess how robust the 260-compound pool is. I ask for the calibration data, a precision/recall analysis against a held-out set, or at least a demonstration that moderate threshold shifts do not substantially change the final conclusions.
  3. [Sec. V, Fig. 4] The main validation beyond the eight benchmarks is Fig. 4, where SEPR and DFPT values of Ξ for 150 screened compounds are described as 'clearly positively correlated'. The figure shows substantial family-dependent scatter, but no correlation coefficient, mean absolute error, or fit is reported. Since the paper's central claim is semi-quantitative agreement, please quantify the correlation and the family-resolved errors (alkali/alkaline-earth, 2p-covalent, transition-metal) so that the reader can judge the strength of the validation.
minor comments (5)
  1. [Abstract and Table II] The phrase 'calculated Tc > 10 K after DFPT verification' should be reconciled with Table II, which lists T_c (exp.) for the experimentally known superconductors. Please report DFPT-computed T_c for all 34 candidates, not only for the newly identified ones.
  2. [Fig. 3 legend] The legend mentions 'computationally difficult' cases, but this category is not defined or discussed in the text. Please clarify what makes a compound computationally difficult.
  3. [Table II note] The table note says some materials are 'only slightly dynamically unstable at ambient pressure but become stable under applied pressure', yet they are labeled dynamically stable candidates. Specify the pressure and other conditions for each entry.
  4. [Eqs. (4)-(5)] The auxiliary matrices G, F, and cM are defined only in the Supplemental Material. To make the main text self-contained, provide at least their physical definitions or a brief derivation sketch.
  5. [Sec. VI, Eq. (8)] The definition of V_ep should be stated explicitly as V_ep = (Ξ^2/N*)^{1/3}; the text's reference to a 'cubic form' as a dimensional normalization is confusing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SEPR is an explicitly approximate screening proxy, and its central claims are checked against independent DFPT calculations.

full rationale

The paper does not present a circular derivation. The SEPR framework is built from three clearly stated approximations (dynamic isotropic, double-center, and the exponential-decay BA model), and Eqs. (3)-(7) are algebraic consequences of those approximations rather than restatements of the screening output. The exponential hopping decay in Eq. (6) is introduced as an assumption, explicitly motivated by the authors' own MattKeyBond framework [30]; even if this self-citation is not wholly independent, the paper does not claim a first-principles theorem for it, and the resulting Ξ/χ values are subsequently compared against DFPT for representative superconductors (Table I) and for 150 screened compounds (Fig. 4). This external comparison is what carries the 'semi-quantitative' claim. The screening thresholds (Ξ>15 meV, χ>125 meV·u^1/2) are described as 'benchmarked' criteria, so they are empirical calibrations rather than derived predictions; however, the final list of 34 candidates is not forced by these thresholds because it is obtained only after full DFPT verification, an independent calculation. The acknowledged family-dependent bias from the uniform L=1.2 Å decay length (Sec. V) is a limitation in accuracy, not a circular reduction of the output to the input. The V_ep–N* decomposition (Eq. 8) is an explicit, dimensionless normalization, and the 'two routes' are an interpretation of the resulting empirical distribution rather than a derivation of the candidates. Overall, the paper's central derivation is self-contained in the sense that the screening metrics are defined from static Hamiltonians and then tested against independent first-principles phonon calculations.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper's central claims rest primarily on the three named approximations (dynamic isotropic, double-center, BA model) and on the choice of a universal decay length and empirically benchmarked thresholds. No new physical entities are posited; V_ep and N* are derived quantities, not postulated entities.

free parameters (4)
  • BA decay length L_A = 1.2 Å
    Uniform exponential decay length in the BA model (Eq. 6) used to convert static hopping integrals into displacement derivatives (Eq. 7). Chosen universally for all elements; directly scales Ξ and χ and is identified as the source of systematic bias in Sec. V.
  • Screening threshold Ξ = 15.0 meV
    Lower cutoff on Ξ in the high-throughput screening (Sec. IV). Described as 'benchmarked criteria,' i.e., fitted to include known superconductors.
  • Screening threshold χ = 125.0 meV·u^1/2
    Lower cutoff on χ in the high-throughput screening (Sec. IV), also benchmarked on known superconductors.
  • Coulomb pseudopotential μ* = 0.1
    Used in McMillan-Allen-Dynes estimates of Tc (Fig. 2 caption and presumably the Tc column in Table II); empirically set.
assumptions (6)
  • domain assumption Exponential decay of hopping integrals with bond length (Eq. 6)
    Assumed in the BA model; motivated by ICOHP bond-length dependence but not derived from first principles.
  • domain assumption Double-center approximation: only directly bonded hopping variations matter; onsite and multicenter variations neglected
    Used in Sec. II B to reduce dH/du to nearest-neighbor bond derivatives.
  • domain assumption Dynamic isotropic approximation: replace phonon mode frequencies by a single average ω̄
    Used in Sec. II A to factor out phonon frequencies; necessary to define Ξ.
  • domain assumption Hellmann-Feynman reasoning: first-order density response does not contribute explicitly; assign bond-length dependence to hopping
    Used in Sec. II C to justify dH/du ≈ -(1/L)(R·e/|R|)H(R).
  • standard math Migdal approximation and double-δ approximation for the phonon self-energy (Eqs. 1-2)
    Standard EPC theory background, cited refs 22-23.
  • domain assumption DFT/PBE electronic structures and DFPT as ground-truth reference
    All calculations rely on semilocal DFT; known limitations for bismuthates are acknowledged in Sec. III.

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Cite this review

Pith. "Pith review of Screening phonon-mediated superconductors from static orbital Hamiltonians." pith.science (2026). https://pith.science/paper/2GFS7HPQ

@misc{pith2026260802426,
  author       = {Pith},
  title        = {Pith review of: Screening phonon-mediated superconductors from static orbital Hamiltonians},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2GFS7HPQ}},
  note         = {Machine review of arXiv:2608.02426}
}
abstract

The first-principles search for superconductors is severely limited by the high cost of electron-phonon coupling (EPC) calculations. Here we develop a low-cost, physically transparent framework that identifies strong-EPC materials directly from static orbital-based Hamiltonians without explicit phonon perturbation calculations. Verification using density functional perturbation theory (DFPT) for representative superconductors shows that the framework captures semi-quantitatively the EPC scale at substantially lower computational cost. Applied to more than 36,000 compounds in the MattKeyBond database, it identifies 34 dynamically stable superconducting candidates with calculated $T_c > 10$ K after DFPT verification. These candidates reveal two distinct routes to relatively high-$T_c$ superconductivity: a metallized covalent $\sigma$-bond route that is more favorable for achieving high-$T_c$ superconductors, and a Fermi-level density-of-states accumulation route that can enhance $T_c$ but usually to a more limited extent.

Figures

Figures reproduced from arXiv: 2608.02426 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of the static electron-phonon response (SEPR) scheme framework. The gray panel shows [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Contour map of the superconducting transition tem [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Comparison of the screening parameter Ξ obtained [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Distribution of the 34 screened dynamically stable superconducting candidates with calculated [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Works this paper leans on

57 extracted references · 2 linked inside Pith

  1. [1]

    Dagotto, Correlated electrons in high-temperature su- perconductors, Rev

    E. Dagotto, Correlated electrons in high-temperature su- perconductors, Rev. Mod. Phys.66, 763 (1994)

    1994

  2. [2]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a mott in- sulator: Physics of high-temperature superconductivity, Rev. Mod. Phys.78, 17 (2006)

    2006

  3. [3]

    Kamihara, T

    Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor LaO 1−xFxFeAs (x= 0.05-0.12) with Tc = 26 K, J. Am. Chem. Soc.130, 3296 (2008)

    2008

  4. [4]

    Ma, Z.-Y

    F. Ma, Z.-Y. Lu, and T. Xiang, Arsenic-bridged antifer- romagnetic superexchange interactions in lafeaso, Phys. Rev. B78, 224517 (2008)

    2008

  5. [5]

    Hsu, J.-Y

    F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W. Huang, P. M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu, D.-C. Yan, and M.-K. Wu, Superconductivity in the PbO-type structureα-FeSe, Proc. Natl. Acad. Sci.105, 14262 (2008)

    2008

  6. [6]

    H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M. Zhang, and M. Wang, Signatures of superconductivity near 80 K in a nickelate under high pressure, Nature621, 493 (2023)

    2023

  7. [7]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Micro- scopic theory of superconductivity, Phys. Rev.106, 162 (1957)

    1957

  8. [8]

    N. W. Ashcroft, Metallic hydrogen: A high-temperature superconductor?, Phys. Rev. Lett.21, 1748 (1968)

    1968

Show all 57 references
  1. [9]

    Somayazulu, M

    M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, and R. J. Hemley, Evidence for superconductivity above 260 K in Lanthanum Superhydride at Megabar Pressures, Phys. Rev. Lett.122, 027001 (2019)

    2019

  2. [10]

    A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Bal- akirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, and M. I. Eremets, Super- conductivity at 250 K in lanthanum hydride under high pressures...

    2019

  3. [11]

    A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Kseno- fontov, and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride sys- tem, Nature525, 73 (2015)

    2015

  4. [12]

    F. Peng, Y. Sun, C. J. Pickard, R. J. Needs, Q. Wu, and Y. Ma, Hydrogen clathrate structures in rare earth hydrides at high pressures: Possible route to room- temperature superconductivity, Phys. Rev. Lett.119, 107001 (2017)

    2017

  5. [13]

    Y. Sun, J. Lv, Y. Xie, H. Liu, and Y. Ma, Route to a superconducting phase above room temperature in electron-doped hydride compounds under high pressure, Phys. Rev. Lett.123, 097001 (2019)

    2019

  6. [14]

    L. Ma, K. Wang, Y. Xie, X. Yang, Y. Wang, M. Zhou, H. Liu, X. Yu, Y. Zhao, H. Wang, G. Liu, and Y. Ma, High-temperature superconducting phase in clathrate calcium hydride CaH 6 up to 215 K at a pressure of 172 GPa, Phys. Rev. Lett.128, 167001 (2022)

    2022

  7. [15]

    Z. Li, X. He, C. Zhang, X. Wang, S. Zhang, Y. Jia, S. Feng, K. Lu, J. Zhao, J. Zhang, B. Min, Y. Long, 11 R. Yu, L. Wang, M. Ye, Z. Zhang, V. Prakapenka, S. Chariton, P. A. Ginsberg, J. Bass, S. Yuan, H. Liu, and C. Jin, Superconductivity above 200 K discovered in su- perhydri...

    2022

  8. [16]

    P. Kong, V. S. Minkov, M. A. Kuzovnikov, A. P. Droz- dov, S. P. Besedin, S. Mozaffari, L. Balicas, F. F. Bal- akirev, V. B. Prakapenka, S. Chariton, D. A. Knyazev, E. Greenberg, and M. I. Eremets, Superconductivity up to 243 K in the yttrium-hydrogen system under high pres- su...

    2021

  9. [17]

    Giustino, Electron-phonon interactions from first prin- ciples, Rev

    F. Giustino, Electron-phonon interactions from first prin- ciples, Rev. Mod. Phys.89, 015003 (2017)

    2017

  10. [18]

    Baroni, S

    S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Gi- annozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001)

    2001

  11. [19]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Giron- coli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, vAnton Kokalj, M. Lazzeri, L. Martin- Samos, N. Marzari,...

    2009

  12. [20]

    W. L. McMillan, Transition temperature of strong- coupled superconductors, Phys. Rev.167, 331 (1968)

    1968

  13. [21]

    P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B12, 905 (1975)

    1975

  14. [22]

    Noffsinger, F

    J. Noffsinger, F. Giustino, B. D. Malone, C.-H. Park, S. G. Louie, and M. L. Cohen, EPW: A program for cal- culating the electron–phonon coupling using maximally localized wannier functions, Comput. Phys. Commun. 181, 2140 (2010)

    2010

  15. [23]

    E. R. Margine and F. Giustino, Anisotropic migdal- eliashberg theory using wannier functions, Physical Re- view B—Condensed Matter and Materials Physics87, 024505 (2013)

    2013

  16. [24]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev.136, B864 (1964)

    1964

  17. [25]

    Kohn and L

    W. Kohn and L. J. Sham, Self-consistent equations in- cluding exchange and correlation effects, Phys. Rev.140, A1133 (1965)

    1965

  18. [26]

    Stanev, C

    V. Stanev, C. Oses, A. G. Kusne, E. Rodriguez, J. Paglione, S. Curtarolo, and I. Takeuchi, Machine learn- ing modeling of superconducting critical temperature, npj Computational Materials4, 29 (2018)

    2018

  19. [27]

    S. R. Xie, Y. Quan, A. C. Hire, B. Deng, J. M. DeStefano, I. Salinas, U. S. Shah, L. Fanfarillo, J. Lim, J. Kim, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld, and R. G. Hennig, Machine learning of superconducting critical temperature from eliashberg theory, npj Computational ...

    2022

  20. [28]

    H. Li, Z. Wang, N. Zou, M. Ye, R. Xu, X. Gong, W. Duan, and Y. Xu, Deep-learning density functional theory hamiltonian for efficient ab initio electronic- structure calculation, Nature Computational Science2, 367 (2022)

    2022

  21. [29]

    Tang, W.-H

    Z. Tang, W.-H. Dong, B. Wu, J.-F. Zhang, Y. Wang, Y. Li, H. Tao, Q. Zeng, C. Wang, C. Si, Z.-Y. Lu, W. Duan, T. Xiang, and Y. Xu, Ai-accelerated metal- lizedσ-bonding screening for superconductor discovery (2026), arXiv:2606.21251 [physics.comp-ph]

    2026 arXiv

  22. [30]

    Zhang, Z.-F

    J.-F. Zhang, Z.-F. Gao, X.-Q. Han, B. Zhan, D. Lv, M. Gao, K. Liu, X. Ren, Z.-Y. Lu, and T. Xiang, Bridging crystal structure and material properties via bond-centric descriptors, arXiv (2026), arXiv:2603.18876 [cond-mat.mtrl-sci]

    2026 arXiv

  23. [31]

    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, Robust zero resistance in a superconducting high-entropy alloy at pressures up to 190 gpa, Proceedings of the Na- tional Academy of Sciences114, 13144 (2017)

    2017

  24. [32]

    J. Guo, G. Lin, S. Cai, C. Xi, C. Zhang, W. Sun, Q. Wang, K. Yang, A. Li, Q. Wu, Y. Zhang, T. Xiang, R. J. Cava, and L. Sun, Record-high superconductivity in niobium–titanium alloy, Advanced Materials31, 1807240 (2019)

    2019

  25. [33]

    Zhang, M

    J.-F. Zhang, M. Gao, K. Liu, and Z.-Y. Lu, First- principles study of the robust superconducting state of nbti alloys under ultrahigh pressures, Phys. Rev. B102, 195140 (2020)

    2020

  26. [34]

    X. Liu, C. Pei, J. Zhang, Q. Wang, N. Li, L. Yan, J. Guan, Y. Wang, M. Li, H. Cheng, H. Lei, K. Liu, Y. Qi, and W. Yang, The record-high robust supercon- ducting temperature of 32 k inα-mob2 under high pres- sure, Materials Today97, 103386 (2026)

    2026

  27. [35]

    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, Rsavs superconductors: Materials with a superconduct- ing state that is robust against large volume shrinkage, Phys. Rev. Mater.4, 071801(R) (2020)

    2020

  28. [36]

    Ozaki, Closest wannier functions to a given set of lo- calized orbitals, Phys

    T. Ozaki, Closest wannier functions to a given set of lo- calized orbitals, Phys. Rev. B110, 125115 (2024)

    2024

  29. [37]

    J. Yu, C. J. Ciccarino, R. Bianco, I. Errea, P. Narang, and B. A. Bernevig, Non-trivial quantum geometry and the strength of electron–phonon coupling, Nature Physics 20, 1262 (2024)

    2024

  30. [38]

    Nagamatsu, N

    J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Superconductivity at 39 K in magne- sium diboride, Nature410, 63 (2001)

    2001

  31. [39]

    J. Han, X. Zhu, J. Zhang, S. Cai, L. Wang, Y. Gao, F. Liu, H. Liu, S. I. Kawaguchi, J. Guo, Y. Zhou, J. Zhao, P. Wang, L. Cao, M. Tian, Q. Wu, T. Xiang, and L. Sun, Superconducting-insulating phase transition in pressur- ized ba1−xkxbio3, Phys. Rev. B111, L020509 (2025)

    2025

  32. [40]

    R. J. Cava, B. Batlogg, J. J. Krajewski, R. Farrow, L. W. Rupp, A. E. White, K. Short, W. F. Peck, and T. Kometani, Superconductivity near 30 k without copper: the ba0.6k0.4bio3 perovskite, Nature332, 814 (1988)

    1988

  33. [41]

    Gavaler, Superconductivity in nb-ge films above 22 k, Applied Physics Letters23, 480 (1973)

    J. Gavaler, Superconductivity in nb-ge films above 22 k, Applied Physics Letters23, 480 (1973)

    1973

  34. [42]

    B. W. Roberts, Survey of superconductive materials and critical evaluation of selected properties, Journal of Phys- ical and Chemical Reference Data5, 581 (1976)

    1976

  35. [43]

    H. J. Choi, D. Roundy, H. Sun, M. L. Cohen, and S. G. Louie, The origin of the anomalous superconduct- ing properties of mgb2, Nature418, 758 (2002)

    2002

  36. [44]

    An and W

    J. An and W. Pickett, Superconductivity of mgb 2: cova- lent bonds driven metallic, Physical Review Letters86, 4366 (2001)

    2001

  37. [45]

    Souma, Y

    S. Souma, Y. Machida, T. Sato, T. Takahashi, H. Mat- sui, S.-C. Wang, H. Ding, A. Kaminski, J. Campuzano, 12 S. Sasaki, et al., The origin of multiple superconducting gaps in mgb2, Nature423, 65 (2003)

    2003

  38. [46]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  39. [47]

    Z. Yin, A. Kutepov, and G. Kotliar, Correlation- enhanced electron-phonon coupling: Applications of gw and screened hybrid functional to bismuthates, chloroni- trides, and other high-t c superconductors, Physical Re- view X3, 021011 (2013)

    2013

  40. [48]

    Z. Li, G. Antonius, M. Wu, F. H. Da Jornada, and S. G. Louie, Electron-phonon coupling from ab initio linear- response theory within the gw method: Correlation- enhanced interactions and superconductivity in ba 1- x k x bio 3, Physical review letters122, 186402 (2019)

    2019

  41. [49]

    G. R. Stewart, Superconductivity in the a15 structure, Physica C: Superconductivity and its Applications514, 28 (2015)

    2015

  42. [50]

    Cucciari and L

    A. Cucciari and L. Boeri, An ab initio answer to long- debated questions about superconducting nb 3 sn, PRX Energy5, 013006 (2026)

    2026

  43. [51]

    S. Y. Savrasov and D. Y. Savrasov, Electron-phonon interactions and related physical properties of metals from linear-response theory, Physical Review B54, 16487 (1996)

    1996

  44. [52]

    A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The materials project: A materials genome approach to accelerating materials innovation, APL Materials1, 011002 (2013)

    2013

  45. [53]

    Zagorac, H

    D. Zagorac, H. M¨ uller, S. Ruehl, J. Zagorac, and S. Rehme, Recent developments in the inorganic crys- tal structure database: theoretical crystal structure data and related features, J. Appl. Cryst.52, 918 (2019)

    2019

  46. [54]

    Weber, S

    F. Weber, S. Rosenkranz, J.-P. Castellan, R. Osborn, R. Hott, R. Heid, K.-P. Bohnen, T. Egami, A. Said, and D. Reznik, Extended phonon collapse and the origin of the charge-density wave in 2 h-nbse 2, Physical review letters107, 107403 (2011)

    2011

  47. [55]

    Zhang, K

    J.-F. Zhang, K. Liu, and Z.-Y. Lu, First-principles study of the double-dome superconductivity in the kagome ma- terial csv 3 sb 5 under pressure, Physical Review B104, 195130 (2021)

    2021

  48. [56]

    Johannes and I

    M. Johannes and I. Mazin, Fermi surface nesting and the origin of charge density waves in metals, Physical Review B—Condensed Matter and Materials Physics77, 165135 (2008)

    2008

  49. [57]

    Dubrovinsky, N

    L. Dubrovinsky, N. Dubrovinskaia, V. B. Prakapenka, and A. M. Abakumov, Implementation of micro-ball nan- odiamond anvils for high-pressure studies above 6 Mbar, Nat. Commun.3, 1163 (2012)

    2012

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