- Open Access
High-throughput superconducting predictions through density of states rescaling
Phys. Rev. B 113, 064507 – Published 17 February, 2026
DOI: https://doi.org/10.1103/82zm-by55
Abstract
First-principles computational methods can predict the superconducting critical temperature 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- systems. In this work, we show that an electron-phonon spectral function calculated at low cost on a coarse grid yields accurate 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.
Physics Subject Headings (PhySH)
Article Text
References (75)
- 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. Pierleoni, A. N. Kolmogorov, N. Rybin, D. Novoselov, V. Anisimov, A. R. Oganov, et al., The 2021 room-temperature superconductivity roadmap, J. Phys.: Condens. Matter 34, 183002 (2022) .
- C. J. Pickard, I. Errea, and M. I. Eremets, Superconducting hydrides under pressure, Annu. Rev. Condens. Matter Phys. 11, 57 (2020).
- G. M. Éliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETP 11, 696 (1960).
- D. J. Scalapino, J. R. Schrieffer, and J. W. Wilkins, Strong-coupling superconductivity. I, Phys. Rev. 148, 263 (1966).
- W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
- P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975).
- L. N. Oliveira, E. K. U. Gross, and W. Kohn, Density-functional theory for superconductors, Phys. Rev. Lett. 60, 2430 (1988) .
- E. R. Margine and F. Giustino, Anisotropic Migdal-Eliashberg theory using Wannier functions, Phys. Rev. B 87, 024505 (2013).
- F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017).
- S. Baroni, S. De Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).
- B. Monserrat, Electron–phonon coupling from finite differences, J. Phys.: Condens. Matter 30, 083001 (2018).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
- D. Duan, H. Yu, H. Xie, and T. Cui, Ab initio approach and its impact on superconductivity, J. Supercond. Novel Magn. 32, 53 (2019).
- A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system, Nature (London) 525, 73 (2015).
- 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 () with high- superconductivity, Sci. Rep. 4, 6968 (2014).
- P. Hou, Z. Huo, and D. Duan, Quantum and anharmonic effects in superconducting under high pressure: A first-principles study, J. Phys. Chem. C 127, 23980 (2023).
- H. Wang, J. S. Tse, K. Tanaka, T. Iitaka, and Y. Ma, Superconductive sodalite-like clathrate calcium hydride at high pressures, Proc. Natl. Acad. Sci. USA 109, 6463 (2012).
- 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).
- H. Liu, I. I. Naumov, R. Hoffmann, N. W. Ashcroft, and R. J. Hemley, Potential high- superconducting lanthanum and yttrium hydrides at high pressure, Proc. Natl. Acad. Sci. USA 114, 6990 (2017).
- 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 (London) 578, 66 (2020).
- 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).
- I. A. Kruglov, D. V. Semenok, H. Song, R. Szczęśniak, I. A. Wrona, R. Akashi, M. M. Davari Esfahani, D. Duan, T. Cui, A. G. Kvashnin, and A. R. Oganov, Superconductivity of and polyhydrides, Phys. Rev. B 101, 024508 (2020).
- A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Balakirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, and M. I. Eremets, Superconductivity at 250 K in lanthanum hydride under high pressures, Nature (London) 569, 528 (2019).
- A. R. Oganov, C. J. Pickard, Q. Zhu, and R. J. Needs, Structure prediction drives materials discovery, Nat. Rev. Mater. 4, 331 (2019).
- C. J. Pickard and R. J. Needs, Structures at high pressure from random searching, Phys. Status Solidi B 246, 536 (2009).
- C. J. Pickard and R. J. Needs, Ab initio random structure searching, J. Phys.: Condens. Matter 23, 053201 (2011).
- 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 superconductivity, Phys. Rev. Lett. 132, 166001 (2024).
- S. Goedecker, Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems, J. Chem. Phys. 120, 9911 (2004).
- A. Sanna, T. F. T. Cerqueira, Y.-W. Fang, I. Errea, A. Ludwig, and M. A. L. Marques, Prediction of ambient pressure conventional superconductivity above 80 K in hydride compounds, npj Comput. Mater. 10, 44 (2024).
- C. Zeni, R. Pinsler, D. Zügner, A. Fowler, M. Horton, X. Fu, Z. Wang, A. Shysheya, J. Crabbé, S. Ueda, R. Sordillo, L. Sun, J. Smith, B. Nguyen, H. Schulz, S. Lewis, C.-W. Huang, Z. Lu, Y. Zhou, H. Yang, et al., A generative model for inorganic materials design, Nature (London) 639, 624 (2025).
- Y. Wang, J. Lv, L. Zhu, and Y. Ma, CALYPSO: A method for crystal structure prediction, Comput. Phys. Commun. 183, 2063 (2012).
- C. W. Glass, A. R. Oganov, and N. Hansen, USPEX—Evolutionary crystal structure prediction, Comput. Phys. Commun. 175, 713 (2006).
- T. Ishikawa, T. Miyake, and K. Shimizu, Materials informatics based on evolutionary algorithms: Application to search for superconducting hydrogen compounds, Phys. Rev. B 100, 174506 (2019).
- D. C. Lonie and E. Zurek, XtalOpt: An open-source evolutionary algorithm for crystal structure prediction, Comput. Phys. Commun. 182, 372 (2011).
- M. J. Hutcheon, A. M. Shipley, and R. J. Needs, Predicting novel superconducting hydrides using machine learning approaches, Phys. Rev. B 101, 144505 (2020).
- A. M. Shipley, M. J. Hutcheon, M. S. Johnson, R. J. Needs, and C. J. Pickard, Stability and superconductivity of lanthanum and yttrium decahydrides, Phys. Rev. B 101, 224511 (2020).
- E. Zurek, Hydrides of the alkali metals and alkaline earth metals under pressure, Comments Inorg. Chem. 37, 78 (2017).
- C. J. Pickard, Ephemeral data derived potentials for random structure search, Phys. Rev. B 106, 014102 (2022).
- 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, J. Chem. Phys. 159, 144801 (2023).
- A. Merchant, S. Batzner, S. S. Schoenholz, M. Aykol, G. Cheon, and E. D. Cubuk, Scaling deep learning for materials discovery, Nature (London) 624, 80 (2023).
- 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, Phys. Rev. B 109, 094117 (2024).
- 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, Phys. Rev. B 99, 064114 (2019).
- F. Giustino, M. L. Cohen, and S. G. Louie, Electron-phonon interaction using Wannier functions, Phys. Rev. B 76, 165108 (2007).
- L. N. Cooper, Bound electron pairs in a degenerate Fermi gas, Phys. Rev. 104, 1189 (1956).
- J. R. Schrieffer, Theory of Superconductivity, Advanced Book Classics (Advanced Book Program, Perseus Books, Reading, MA, 1999).
- K. Trachenko, B. Monserrat, M. Hutcheon, and C. J. Pickard, Upper bounds on the highest phonon frequency and superconducting temperature from fundamental physical constants, J. Phys.: Condens. Matter 37, 165401 (2025).
- C. J. Pickard and M. C. Payne, Extrapolative approaches to Brillouin-zone integration, Phys. Rev. B 59, 4685 (1999).
- 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 analyze a density of states, Mater. Today Electron. 1, 100002 (2022).
- Y. Quan and W. E. Pickett, Van Hove singularities and spectral smearing in high-temperature superconducting , Phys. Rev. B 93, 104526 (2016).
- T. Koretsune and R. Arita, Efficient method to calculate the electron–phonon coupling constant and superconducting transition temperature, Comput. Phys. Commun. 220, 239 (2017).
- C. Morice, R. Akashi, T. Koretsune, S. S. Saxena, and R. Arita, Weak phonon-mediated pairing in superconductor from first principles, Phys. Rev. B 95, 180505(R) (2017).
- C. Pellegrini and A. Sanna, Ab initio methods for superconductivity, Nat. Rev. Phys. 6, 509 (2024).
- P. B. Allen and B. Mitrović, Theory of superconducting Tc, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1983), Vol. 37, pp. 1–92.
- 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 Comput. Mater. 8, 14 (2022).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, 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, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- M. Wierzbowska, S. d. Gironcoli, and P. Giannozzi, Origins of low- and high-pressure discontinuities of in niobium, arXiv:cond-mat/0504077.
- 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, Comput. Phys. Commun. 185, 1477 (2014).
- R. J. Nicholls, A. J. Morris, C. J. Pickard, and J. R. Yates, OptaDOS - a new tool for EELS calculations, J. Phys.: Conf. Ser. 371, 012062 (2012).
- C. J. Pickard and M. C. Payne, Second-order k p perturbation theory with Vanderbilt pseudopotentials and plane waves, Phys. Rev. B 62, 4383 (2000).
- P. E. Blöchl, O. Jepsen, and O. K. Andersen, Improved tetrahedron method for Brillouin-zone integrations, Phys. Rev. B 49, 16223 (1994).
- M. Kawamura, Y. Gohda, and S. Tsuneyuki, Improved tetrahedron method for the Brillouin-zone integration applicable to response functions, Phys. Rev. B 89, 094515 (2014).
- O. Jepson and O. K. Anderson, The electronic structure of h.c.p. Ytterbium, Solid State Commun. 9, 1763 (1971).
- M. Y. Toriyama, A. M. Ganose, M. Dylla, S. Anand, J. Park, M. K. Brod, J. Munro, K. A. Persson, A. Jain, and G. J. Snyder, Comparison of the tetrahedron method to smearing methods for the electronic density of states, arXiv:2103.03469.
- D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013) .
- M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G. M. Rignanese, The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
- C. Pellegrini, C. Kukkonen, and A. Sanna, Ab initio calculations of superconducting transition temperatures: When going beyond RPA is essential, Phys. Rev. B 108, 064511 (2023).
- E. Kogler, D. Spath, R. Lucrezi, H. Mori, Z. Zhu, Z. Li, E. R. Margine, and C. Heil, IsoME: Streamlining high-precision Eliashberg calculations, Comput. Phys. Commun. 315, 109720 (2025).
- D. K. Finnemore, T. F. Stromberg, and C. A. Swenson, Superconducting properties of high-purity niobium, Phys. Rev. 149, 231 (1966).
- P. B. Allen, Empirical electron-phonon values from resistivity of cubic metallic elements, Phys. Rev. B 36, 2920 (1987).
- K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- 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 superconductor, Phys. Rev. Lett. 114, 157004 (2015) .
- 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. Margine, and F. Giustino, Electron–phonon physics from first principles using the EPW code, npj Comput. Mater. 9, 156 (2023).
- W. Sano, T. Koretsune, T. Tadano, R. Akashi, and R. Arita, Effect of van Hove singularities on high- superconductivity in H3S, Phys. Rev. B 93, 094525 (2016).
- 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, Commun. Phys. 7, 33 (2024).
- K. Bozier, K. Wang, B. Montserrat, and C. J. Pickard, High-throughput superconducting through density of states rescaling [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.18519011.