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REVIEW 2 major objections 5 minor 72 references

High-throughput superconducting $T_{\mathrm{c}}$ predictions through density of states rescaling

T0 review · 2 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Rescaling the Fermi density of states makes coarse-grid Tc predictions accurate.

desk verdict A cheap, physically motivated DOS rescaling that clearly helps sharp-DOS superconductors like Mg2IrH6 and H3S, honestly caveated by the authors, but with no criterion for when it fails. read the letter →

arxiv 2508.18371 v1 pith:C7XYD6CR submitted 2025-08-25 cond-mat.supr-con cond-mat.mtrl-sciphysics.comp-ph

Kieran Bozier , Kang Wang , Bartomeu Monserrat , Chris J. Pickard This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sciphysics.comp-ph
keywords superconductivityelectron-phononcouplingdensityofstatestransitiontemperatureEliashbergtheoryhigh-throughputscreeningcoarsegridshydrides
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 argues that the biggest obstacle to cheap, high-throughput predictions of superconducting transition temperatures is not the electron-phonon coupling calculation itself but how the coarse Brillouin-zone grid misestimates the electronic density of states at the Fermi energy. It proposes a post-processing correction: take the electron-phonon spectral function α²F(ω) computed with standard Gaussian smearing on a coarse grid and multiply it by the ratio of an accurate tetrahedra DOS at the Fermi level to the Gaussian-smeared DOS. On systems with sharp density-of-states peaks near the Fermi energy—precisely the systems most likely to be high-Tc—this restores Tc values that otherwise require very dense grids. The paper shows Mg2IrH6, whose Fermi energy sits on a sharp peak, recovering its converged ~160 K Tc even on a 2³ phonon grid, whereas the standard method underestimates it badly. If correct, this gives screening pipelines a nearly free way to avoid discarding promising high-Tc candidates early.

What carries the argument

The key object is the density-of-states rescaling factor g = f_NF / N_F(σ), applied at the level of the surface-averaged electron-phonon spectral function α²F(ω) and hence to λ. The factor is motivated by the fact that α²F and λ are linearly proportional to the Fermi-level DOS NF; replacing the unreliable Gaussian-smeared value with a tetrahedra value removes the dominant smearing dependence. It does work at almost no additional cost because a converged DOS is typically already computed in screening workflows, and it acts as a post-processing correction rather than requiring new electron-phonon calculations.

What would settle it

Take a superconductor with a sharp DOS peak at the Fermi energy, compute Tc with the rescaled coarse-grid method, and compare against a fully converged calculation that resolves the DOS shape, for example variable-DOS Eliashberg on fine grids. If the rescaled Tc overshoots by much more than the standard method's underestimate, the multiplicative-DOS assumption is the culprit. Alternatively, compute λ on coarse and fine grids and check whether the ratio λ_coarse / λ_fine tracks N_F(σ) / f_NF.

Watch

Extended reading notes

Core claim

The central claim is that the coarse-grid error in the Eliashberg spectral function is dominated by a multiplicative error in the Fermi-level density of states, so rescaling α²F(ω) by f_NF / N_F(σ) corrects most of the error without refining the grid. Here f_NF is a high-quality DOS from the tetrahedra method and N_F(σ) is the DOS from the Gaussian smearing used in the Tc calculation. In the idealized constant-matrix-element limit this correction is exact, because the coupling λ is then simply proportional to NF. Across six test systems, the rescaling flattens Tc as a function of smearing and accelerates convergence with grid size; the effect is largest when the Fermi energy sits on a sharp

Load-bearing premise

The coarse-grid error in the electron-phonon spectral function is mostly a multiplicative error in the Fermi-level density of states, so a single scalar rescaling can fix it; this is exact only when the electron-phonon matrix elements are effectively constant near the Fermi surface.

Editorial extensions

If this is right

  • Coarse-grid Tc estimates become reliable enough for early-stage screening, so candidates with sharp DOS peaks survive the first pass.
  • The method removes the need for very fine electronic k grids, and because k and q grids are often linked, coarser phonon q grids can be used too.
  • Comparing standard and rescaled curves gives a diagnostic: if rescaling changes Tc strongly, DOS convergence is the bottleneck; if not, matrix-element convergence dominates.
  • Systems with Fermi energy on a DOS peak may be overestimated by constant-DOS Eliashberg even after rescaling, pushing the workflow toward variable-DOS Eliashberg for final validation.
  • The correction is general and can be inserted into existing screening pipelines as a post-processing step with negligible cost.

Reading between the lines

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

  • Beyond the paper: the same rescaling idea could be applied to other Fermi-surface-weighted quantities, such as transport coefficients or magnetic response, wherever coarse-grid Gaussian weighting is used.
  • Beyond the paper: a screening heuristic could flag candidates where f_NF / N_F(σ) deviates strongly from unity, since those are the systems whose Tc ranking is most likely wrong under standard methods.
  • Beyond the paper: the failure mode suggests a practical trust criterion—use rescaling when electron-phonon matrix elements vary smoothly near the Fermi surface, and validate with a small set of fine-grid calculations.
  • Beyond the paper: the scalar rescaling factor could be generalized to a frequency-dependent or k-dependent correction that also accounts for matrix-element variation, though the paper does not do this.
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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

2 major / 5 minor

Summary. The paper proposes a post-processing rescaling of the Eliashberg spectral function alpha^2 F(omega) computed on coarse Brillouin-zone grids. The rescaling factor is f_NF / N_F(sigma), where f_NF is a high-quality tetrahedra density of states at the Fermi energy and N_F(sigma) is the Gaussian-smearing value used in the Tc calculation. The idea, building on Refs. [50,51], is that the dominant coarse-grid error in alpha^2 F and lambda is a multiplicative error in the Fermi-level DOS, so a scalar prefactor corrects it. The method is tested on Al, Nb, H3S, CaH6, LaH10, and Mg2IrH6. For sharp-DOS systems such as H3S and especially Mg2IrH6, the rescaling reduces the smearing dependence and yields converged Tc values on coarse grids, including ~160 K for Mg2IrH6 on a 2^3 phonon grid. LaH10 is identified as a counterexample where the default Gaussian method benefits from error cancellation and rescaling slightly worsens the result. The authors recommend plotting both default and rescaled curves and discuss limitations of the constant-DOS Eliashberg approximation.

Significance. If the central claim is accepted, the method is a cheap, parameter-free post-processing correction (the only free parameter being the usual mu*) that could be integrated into high-throughput superconducting screening, particularly for systems with sharp DOS features, which are often the most promising high-Tc candidates. The paper is honest about limitations and documents a failure mode, which is a strength. The method is physically motivated and simple to implement, and the benchmark set includes literature-converged systems such as H3S and LaH10. However, the validation is limited to six systems, the strongest success is benchmarked against a prior calculation from the same group, and no quantitative criterion is provided for when the multiplicative rescaling assumption holds. This makes the generality of the abstract claim undersupported. The contribution is incremental relative to Refs. [50,51] but the explicit focus on high-throughput screening and the Mg2IrH6 demonstration give it practical value.

major comments (2)
  1. [Sec. III B, Eq. (5), Sec. IV] The rescaling is exact only when alpha^2 F(omega,sigma) is proportional to N_F(sigma) with a sigma-independent prefactor, i.e., in the constant-matrix-element, constant-phonon-frequency limit. The paper itself shows this fails for LaH10 (Fig. 3(e), Fig. 6), where rescaling slightly worsens a well-converged default result. The stated condition of 'weak momentum and energy dependence' of |g_nmnu(k,k')|^2 is descriptive, not a screening rule. Because the stated application is high-throughput screening, in which each candidate cannot be individually inspected, the central claim that the rescaled spectral function 'yields accurate Tc predictions' needs either a quantitative diagnostic (e.g., comparing the sigma-dependence of lambda before and after rescaling, or a measure of matrix-element variation) or a clear statement that the rescaling is a heuristic to be used alongside the default curve
  2. [Sec. III D/E, Figs. 3-6] The validation set is only six systems, and the flagship success, Mg2IrH6, is benchmarked against Ref. [27], a prior calculation from the same group. The claim that 'even 2^3 grids reproduce the converged value of 160 K' is demonstrated for a single compound. For a method proposed for high-throughput use, the reader needs at least an indication of false-positive/false-negative behavior over a range of DOS shapes and matrix-element characters. I am not requesting an exhaustive benchmark, but without a broader set or a worst-case bound, the domain of applicability remains underspecified.
minor comments (5)
  1. [Eq. (4)] The Gaussian broadening expression is missing a minus sign in the exponent: it should be exp(-epsilon^2/sigma^2).
  2. [Acknowledgments] Typo: 'ESPRC' should be 'EPSRC'.
  3. [Sec. III E, Figs. 4-6] 'an 83 phonon grid' should read 'an 8^3 phonon grid'; similar notation is used inconsistently for other grids.
  4. [Fig. 3 caption] The caption states 'the density of states of the primitive cell' while the text refers to the conventional cell visualized with VESTA; clarify which cell is used for the DOS plot.
  5. [Sec. III B] The sentence 'use this to replace the value obtained by the Gaussian smearing' is imprecise: the rescaling multiplies alpha^2 F by a ratio rather than directly replacing N_F in the calculation. This could be clarified to avoid confusion about the implementation.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the DOS-rescaling method is a parameter-free correction derived from the explicit linear dependence of alpha^2F on N_F, and its central claims are validated against multiple external benchmarks; the only self-citation (Mg2IrH6) is a non-load-bearing benchmark.

full rationale

The paper's derivation chain is self-contained at the level of the method itself. Equation (5) defines the rescaled spectral function as g(alpha^2F)(omega,sigma) = [fN_F / N_F(sigma)] alpha^2F(omega,sigma), which directly follows from the explicit proportionality of alpha^2F to the Fermi-level density of states in Eqs. (1)-(3). No parameter is fitted to any target T_c: fN_F is obtained from an accurate tetrahedra DOS calculation, N_F(sigma) is the Gaussian-smearing DOS used in the coarse calculation, and the rescaling is a deterministic post-processing step. The idealized constant-matrix-element limit in Eq. (6) is presented as an explanatory limiting case, not as the derivation of the method's general validity, and the paper explicitly acknowledges that a scalar prefactor cannot correct smearing-induced reshaping of the matrix-element sampling. The LaH10 case is reported as a limitation where the default Gaussian method benefits from error cancellation and rescaling slightly worsens the result, and the authors recommend plotting both curves; this is an honest caveat, not a circular step. The comparison of Mg2IrH6 to Ref. [27] does cite prior work sharing an author (C.J. Pickard), but this is a benchmark rather than a load-bearing premise: the central claim does not reduce to that citation, and the same rescaling behavior is demonstrated against externally established systems including H3S, LaH10, Nb, Al, and CaH6. The stated limitations about possible overestimation for sharp DOS peaks in constant-DOS Eliashberg calculations are also caveats about the underlying theory, not circularity. Overall, no circular step can be identified; the score reflects only the minor presence of a non-load-bearing self-citation in the Mg2IrH6 benchmark.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical entities. The only input parameter is the fixed mu* = 0.125; the rescaling factor is computed from converged DOS and is not a fitted parameter.

free parameters (1)
  • Coulomb pseudopotential mu* = 0.125 (fixed)
    Chosen by hand as a common convention; not computed from the screened Coulomb interaction, so Tc values depend on this choice.
assumptions (4)
  • domain assumption Isotropic constant-DOS Eliashberg equations provide the correct Tc for the tested systems
    Used throughout Sec III-IV; the authors note this approximation can overestimate Tc when the DOS has sharp peaks near E_F (Sec IV), citing Ref [71].
  • domain assumption The tetrahedra DOS f_NF is essentially converged and the Gaussian-smeared N_F(sigma) on the same grid captures the DOS error multiplicatively
    This is the load-bearing premise of Eq 5; it holds exactly only in the constant-matrix-element limit of Eq 6, and the authors show it breaks down for LaH10 (Sec IV).
  • standard math alpha^2 F(omega) and lambda are linearly proportional to N_F
    Follows from Eqs 1-3; standard electron-phonon theory.
  • domain assumption PBE/pseudopotential DFT and Quantum Espresso phonon calculations adequately describe the tested materials
    Computational setup in Sec III A; not justified beyond prior usage.

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Cite this review

Pith. "Pith review of High-throughput superconducting $T_{\mathrm{c}}$ predictions through density of states rescaling." pith.science (2026). https://pith.science/paper/C7XYD6CR

@misc{pith2026250818371,
  author       = {Pith},
  title        = {Pith review of: High-throughput superconducting $T_\mathrmc$ predictions through density of states rescaling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C7XYD6CR}},
  note         = {Machine review of arXiv:2508.18371}
}
abstract

First principles computational methods can predict the superconducting critical temperature $T_{\mathrm{c}}$ of conventional superconductors through the electron-phonon spectral function. Full convergence of this quantity requires Brillouin zone integration on very dense grids, presenting a bottleneck to high-throughput screening for high $T_{\mathrm{c}}$ systems. In this work, we show that an electron-phonon spectral function calculated at low cost on a coarse grid yields accurate $T_{\mathrm{c}}$ predictions, provided the function is rescaled to correct for the inaccurate value of the density of states at the Fermi energy on coarser grids. Compared to standard approaches, the method converges rapidly and improves the accuracy of predictions for systems with sharp features in the density of states. This approach can be directly integrated into existing materials screening workflows, enabling the rapid identification of promising candidates that might otherwise be overlooked.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 66 canonical work pages

  1. [27]

    Dolui, L

    K. Dolui, L. J. Conway, C. Heil, T. A. Strobel, R. P. Prasankumar, and C. J. Pickard, Feasible Route to High- Temperature Ambient-Pressure Hydride Superconduc- tivity, Physical Review Letters132, 166001 (2024)

    work page 2024

  2. [1]

    Boeri, R

    L. Boeri, R. Hennig, P. Hirschfeld, G. Profeta, A. Sanna, E. Zurek, W. E. Pickett, M. Amsler, R. Dias, M. I. Eremets, C. Heil, R. J. Hemley, H. Liu, Y. Ma, C. Pier- leoni, A. N. Kolmogorov, N. Rybin, D. Novoselov, V. Anisimov, A. R. Oganov, C. J. Pickard, T. Bi, R. Arita, I. Errea, C. Pellegrini, R. Requist, E. K. U. Gross, E. R. Margine, S. R. Xie, Y. Qu...

    work page 2021

  3. [2]

    C. J. Pickard, I. Errea, and M. I. Eremets, Superconduct- ing Hydrides Under Pressure, Annual Review of Con- densed Matter Physics11, 57 (2020), publisher: Annual Reviews Type: Journal Article

    work page 2020

  4. [3]

    M., Interactions between electrons and lattice vibrations in a superconductor., J

    Éliashberg, G. M., Interactions between electrons and lattice vibrations in a superconductor., J. Exp. Theor. Phys. 38, 966 (1960)

    work page 1960

  5. [4]

    D. J. Scalapino, J. R. Schrieffer, and J. W. Wilkins, Strong-Coupling Superconductivity. I, Physical Review 148, 263 (1966)

    work page 1966

  6. [5]

    W. L. McMillan, Transition Temperature of Strong- Coupled Superconductors, Physical Review 167, 331 (1968)

    work page 1968

  7. [6]

    P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Physical Re- view B 12, 905 (1975)

    work page 1975

  8. [7]

    L. N. Oliveira, E. K. U. Gross, and W. Kohn, Density- Functional Theory for Superconductors, Physical Review Letters 60, 2430 (1988), publisher: American Physical Society

    work page 1988

Show all 72 references
  1. [8]

    E. R. Margine and F. Giustino, Anisotropic Migdal- Eliashberg theory using Wannier functions, Physical Re- view B 87, 024505 (2013)

    2013

  2. [9]

    Giustino, Electron-phonon interactions from first prin- ciples, Reviews of Modern Physics89, 015003 (2017)

    F. Giustino, Electron-phonon interactions from first prin- ciples, Reviews of Modern Physics89, 015003 (2017)

    2017

  3. [10]

    Baroni, S

    S. Baroni, S. De Gironcoli, A. Dal Corso, and P. Gi- annozzi, Phonons and related crystal properties from density-functional perturbation theory, Reviews of Mod- ern Physics 73, 515 (2001)

    2001

  4. [11]

    Monserrat, Electron–phonon coupling from finite dif- ferences, Journal of Physics: Condensed Matter 30, 083001 (2018)

    B. Monserrat, Electron–phonon coupling from finite dif- ferences, Journal of Physics: Condensed Matter 30, 083001 (2018). 9

    2018

  5. [12]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity, Physical Review108, 1175 (1957), publisher: American Physical Society

    1957

  6. [13]

    D. Duan, H. Yu, H. Xie, and T. Cui, Ab Initio Approach and Its Impact on Superconductivity, Journal of Super- conductivity and Novel Magnetism32, 53 (2019)

    2019

  7. [14]

    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, Nature 525, 73 (2015), publisher: Nature Publish- ing Group

    2015

  8. [15]

    D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, and T. Cui, Pressure-induced metallization of dense (H2S)2H2 with high-Tc supercon- ductivity, Scientific Reports4, 6968 (2014)

    2014

  9. [16]

    P. Hou, Z. Huo, and D. Duan, Quantum and Anhar- monic Effects in Superconducting Im 3m CaH6 Under High Pressure: A First-Principles Study, The Journal of Physical Chemistry C 127, 23980 (2023), publisher: American Chemical Society

    2023

  10. [17]

    H. Wang, J. S. Tse, K. Tanaka, T. Iitaka, and Y. Ma, Superconductive sodalite-like clathrate calcium hydride at high pressures, Proceedings of the National Academy of Sciences 109, 6463 (2012), publisher: Proceedings of the National Academy of Sciences

    2012

  11. [18]

    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, Physical Review Letters 119, 107001 (2017), publisher: American Physical Soci- ety

    2017

  12. [19]

    H. Liu, I. I. Naumov, R. Hoffmann, N. W. Ashcroft, and R. J. Hemley, Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure, Pro- ceedings of the National Academy of Sciences114, 6990 (2017), publisher: Proceedings of the National Academy of Sciences

    2017

  13. [20]

    Errea, F

    I. Errea, F. Belli, L. Monacelli, A. Sanna, T. Koretsune, T. Tadano, R. Bianco, M. Calandra, R. Arita, F. Mauri, and J. A. Flores-Livas, Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride, Nature 578, 66 (2020)

    2020

  14. [21]

    Somayazulu, M

    M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, and R. J. Hem- ley, Evidence for Superconductivity above 260 K in Lan- thanum Superhydride at Megabar Pressures, Physical Review Letters122, 027001 (2019), publisher: American Physical Society

    2019

  15. [22]

    I. A. Kruglov, D. V. Semenok, H. Song, R. Szczęś- niak, I. A. Wrona, R. Akashi, M. M. Davari Esfahani, D. Duan, T. Cui, A. G. Kvashnin, and A. R. Oganov, Superconductivity of ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaH}}_{16}$ polyhydrides, Physical Re- viewB 101,024508(2020),publ...

    2020

  16. [23]

    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

  17. [24]

    A. R. Oganov, C. J. Pickard, Q. Zhu, and R. J. Needs, Structure prediction drives materials discovery, Nature Reviews Materials4, 331 (2019), publisher: Nature Pub- lishing Group

    2019

  18. [25]

    C. J. Pickard and R. J. Needs, Structures at high pressure from random searching, phys- ica status solidi (b) 246, 536 (2009), _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssb.200880546

    2009 doi

  19. [26]

    C. J. Pickard and R. J. Needs, Ab initio random struc- ture searching, Journal of Physics: Condensed Matter 23, 053201 (2011)

    2011

  20. [28]

    S. Goedecker, Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems, The Journal of Chemical Physics 120, 9911 (2004)

    2004

  21. [29]

    Sanna, T

    A. Sanna, T. F. T. Cerqueira, Y.-W. Fang, I. Errea, A. Ludwig, and M. A. L. Marques, Prediction of am- bient pressure conventional superconductivity above 80 K in hydride compounds, npj Computational Materials 10, 1 (2024), publisher: Nature Publishing Group

    2024

  22. [30]

    C. Zeni, R. Pinsler, D. Zügner, A. Fowler, M. Horton, X. Fu, Z. Wang, A. Shysheya, J. Crabbé, S. Ueda, R. Sor- dillo, L. Sun, J. Smith, B. Nguyen, H. Schulz, S. Lewis, C.-W. Huang, Z. Lu, Y. Zhou, H. Yang, H. Hao, J. Li, C. Yang, W. Li, R. Tomioka, and T. Xie, A generative mod...

    2025

  23. [31]

    Y. Wang, J. Lv, L. Zhu, and Y. Ma, CALYPSO: A method for crystal structure prediction, Computer Physics Communications 183, 2063 (2012)

  24. [32]

    C. W. Glass, A. R. Oganov, and N. Hansen, US- PEX—Evolutionary crystal structure prediction, Com- puter Physics Communications175, 713 (2006)

    2006

  25. [33]

    Ishikawa, T

    T. Ishikawa, T. Miyake, and K. Shimizu, Materials infor- matics based on evolutionary algorithms: Application to search for superconducting hydrogen compounds, Phys- ical Review B 100, 174506 (2019), publisher: American Physical Society

    2019

  26. [34]

    D. C. Lonie and E. Zurek, XtalOpt: An open-source evolutionary algorithm for crystal structure prediction, Computer Physics Communications182, 372 (2011)

    2011

  27. [35]

    M. J. Hutcheon, A. M. Shipley, and R. J. Needs, Predict- ing novel superconducting hydrides using machine learn- ing approaches, Physical Review B101, 144505 (2020)

    2020

  28. [36]

    A. M. Shipley, M. J. Hutcheon, M. S. Johnson, R. J. Needs,andC.J.Pickard,Stabilityandsuperconductivity of lanthanum and yttrium decahydrides, Physical Review B 101, 224511 (2020)

    2020

  29. [37]

    E. Zurek, Hydrides of the Alkali Metals and Alkaline Earth Metals Under Pressure, Comments on Inorganic Chemistry 37, 78 (2017), publisher: Taylor & Francis _eprint: https://doi.org/10.1080/02603594.2016.1196679

    2017

  30. [38]

    C. J. Pickard, Ephemeral data derived potentials for ran- dom structure search, Physical Review B 106, 014102 (2022), publisher: American Physical Society

    2022

  31. [39]

    P.T.Salzbrenner, S.H.Joo, L.J.Conway, P.I.C.Cooke, B. Zhu, M. P. Matraszek, W. C. Witt, and C. J. Pickard, Developments and further applications of ephemeral data derived potentials, The Journal of Chemical Physics159, 144801 (2023)

    2023

  32. [40]

    Merchant, S

    A. Merchant, S. Batzner, S. S. Schoenholz, M. Aykol, G. Cheon, and E. D. Cubuk, Scaling deep learning for 10 materials discovery, Nature 624, 80 (2023), publisher: Nature Publishing Group

    2023

  33. [41]

    Z. Wang, X. Wang, X. Luo, P. Gao, Y. Sun, J. Lv, H. Wang, Y. Wang, and Y. Ma, Concurrent learning scheme for crystal structure prediction, Physical Review B 109, 094117 (2024), publisher: American Physical So- ciety

    2024

  34. [42]

    E. V. Podryabinkin, E. V. Tikhonov, A. V. Shapeev, and A. R. Oganov, Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning,PhysicalReviewB 99,064114(2019),publisher: American Physical Society

    2019

  35. [43]

    Giustino, M

    F. Giustino, M. L. Cohen, and S. G. Louie, Electron- phononinteractionusingWannierfunctions,PhysicalRe- view B 76, 165108 (2007)

    2007

  36. [44]

    L. N. Cooper, Bound Electron Pairs in a Degenerate Fermi Gas, Physical Review104, 1189 (1956)

    1956

  37. [45]

    J. R. Schrieffer, Theory of superconductivity , Advanced book classics (Advanced Book Program, Perseus Books, Reading, Mass, 1999)

    1999

  38. [46]

    Trachenko, B

    K. Trachenko, B. Monserrat, M. Hutcheon, and C. J. Pickard, Upper bounds on the highest phonon fre- quency and superconducting temperature from funda- mental physical constants, Journal of Physics: Con- densed Matter 37, 165401 (2025), publisher: IOP Pub- lishing

    2025

  39. [47]

    C. J. Pickard and M. C. Payne, Extrapolative approaches to Brillouin-zone integration, Physical Review B59, 4685 (1999)

    1999

  40. [48]

    M. Y. Toriyama, A. M. Ganose, M. Dylla, S. Anand, J. Park, M. K. Brod, J. M. Munro, K. A. Persson, A. Jain, and G. J. Snyder, How to analyse a density of states, Materials Today Electronics1, 100002 (2022)

    2022

  41. [49]

    Quan and W

    Y. Quan and W. E. Pickett, Van Hove singularities and spectral smearing in high-temperature superconducting ${\mathrm{H}}_{3}\mathrm{S}$, Physical Review B 93, 104526 (2016), publisher: American Physical Society

    2016

  42. [50]

    Koretsune and R

    T. Koretsune and R. Arita, Efficient method to calculate the electron–phonon coupling constant and supercon- ducting transition temperature, Computer Physics Com- munications 220, 239 (2017)

    2017

  43. [51]

    Morice, R

    C. Morice, R. Akashi, T. Koretsune, S. S. Saxena, and R. Arita, Weak phonon-mediated pairing in BiS 2 super- conductor from first principles, Physical Review B 95, 180505 (2017)

    2017

  44. [52]

    Pellegrini and A

    C. Pellegrini and A. Sanna, Ab initio methods for su- perconductivity, Nature Reviews Physics6, 509 (2024), publisher: Nature Publishing Group

    2024

  45. [53]

    P. B. Allen and B. Mitrović, Theory of Superconducting Tc, in Solid State Physics , Vol. 37, edited by H. Ehren- reich, F. Seitz, and D. Turnbull (Academic Press, 1983) pp. 1–92

    1983

  46. [54]

    Salinas, U

    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, Machinelearningofsuperconductingcriticaltemperature from Eliashberg theory, npj Computational Materials8, 1...

    2022

  47. [55]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. ...

    2009

  48. [56]

    Wierzbowska, S

    M. Wierzbowska, S. d. Gironcoli, and P. Giannozzi, Ori- gins of low- and high-pressure discontinuities of $T_{c}$ in niobium (2006), arXiv:cond-mat/0504077

    2006 arXiv

  49. [57]

    A. J. Morris, R. J. Nicholls, C. J. Pickard, and J. R. Yates, OptaDOS: A tool for obtaining density of states, core-level and optical spectra from electronic structure codes, Computer Physics Communications 185, 1477 (2014)

    2014

  50. [58]

    R. J. Nicholls, A. J. Morris, C. J. Pickard, and J. R. Yates, OptaDOS - a new tool for EELS calculations, Journal of Physics: Conference Series 371, 012062 (2012)

    2012

  51. [59]

    C. J. Pickard and M. C. Payne, Second-order k· p per- turbation theory with Vanderbilt pseudopotentials and plane waves, Physical Review B62, 4383 (2000)

    2000

  52. [60]

    P. E. Blöchl, O. Jepsen, and O. K. Andersen, Im- proved tetrahedron method for Brillouin-zone integra- tions, Physical Review B49, 16223 (1994)

    1994

  53. [61]

    Kawamura, Y

    M. Kawamura, Y. Gohda, and S. Tsuneyuki, Improved tetrahedronmethodfortheBrillouin-zoneintegrationap- plicable to response functions, Physical Review B 89, 094515 (2014)

    2014

  54. [62]

    D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Physical Review B88, 085117 (2013), publisher: American Physical Society

    2013

  55. [63]

    M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G. M. Rig- nanese, The PseudoDojo: Training and grading a 85 ele- ment optimized norm-conserving pseudopotential table, Computer Physics Communications226, 39 (2018)

    2018

  56. [64]

    Pellegrini, C

    C. Pellegrini, C. Kukkonen, and A. Sanna, Ab initio calculations of superconducting transition temperatures: When going beyond RPA is essential, Physical Review B 108, 064511 (2023)

    2023

  57. [65]

    Kogler, D

    E. Kogler, D. Spath, R. Lucrezi, H. Mori, Z. Zhu, Z. Li, E. R. Margine, and C. Heil, IsoME: Streamlining high-precisionEliashbergcalculations,ComputerPhysics Communications 315, 109720 (2025)

    2025

  58. [66]

    D. K. Finnemore, T. F. Stromberg, and C. A. Swen- son, Superconducting Properties of High-Purity Nio- bium, Physical Review149, 231 (1966)

    1966

  59. [67]

    P. B. Allen, Empirical electron-phononλ values from re- sistivity of cubic metallic elements, Physical Review B 36, 2920 (1987)

    1987

  60. [68]

    K.MommaandF.Izumi,VESTA3forthree-dimensional visualization of crystal, volumetric and morphology data, JournalofAppliedCrystallography 44,1272(2011),pub- lisher: International Union of Crystallography

    2011

  61. [69]

    Errea, M

    I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, and F. Mauri, High-Pressure Hydrogen Sulfide from First Principles: A Strongly Anharmonic Phonon-Mediated Superconduc- tor, Physical Review Letters 114, 157004 (2015), pub- lisher: Am...

    2015

  62. [70]

    H. Lee, S. Poncé, K. Bushick, S. Hajinazar, J. Lafuente- Bartolome, J. Leveillee, C. Lian, J.-M. Lihm, F. Macheda, H. Mori, H. Paudyal, W. H. Sio, S. Tiwari, M. Zacharias, X. Zhang, N. Bonini, E. Kioupakis, E. R. 11 Margine, and F. Giustino, Electron–phonon physics from first ...

    2023

  63. [71]

    W. Sano, T. Koretsune, T. Tadano, R. Akashi, and R. Arita, Effect of van Hove singularities on high-Tc su- perconductivity in H3S, Physical Review B93, 094525 (2016), arXiv:1512.07365 [cond-mat]

    2016 arXiv

  64. [72]

    Lucrezi, P

    R. Lucrezi, P. P. Ferreira, S. Hajinazar, H. Mori, H. Paudyal, E. R. Margine, and C. Heil, Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides, Communications Physics7, 33 (2024), publisher: Nature Publishing Group

    2024

Pith tools

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