Machine learning of superconducting critical temperature from Eliashberg theory
Abstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c. McMillan, Allen, and Dynes derived approximate closed-form...
| Main Authors: | , , , , , , , , , , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-01-01
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| Series: | npj Computational Materials |
| Online Access: | https://doi.org/10.1038/s41524-021-00666-7 |
| _version_ | 1819281552098459648 |
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| author | 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 R. G. Hennig |
| author_facet | 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 R. G. Hennig |
| author_sort | S. R. Xie |
| collection | DOAJ |
| description | Abstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c. McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α 2 F(ω). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α 2 F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α 2 F functions and numerical solutions of the Eliashberg equations, we derive a formula for T c that performs as well as Allen–Dynes for low-T c superconductors and substantially better for higher-T c ones. This corrects the systematic underestimation of T c while reproducing the physical constraints originally outlined by Allen and Dynes. This equation should replace the Allen–Dynes formula for the prediction of higher-temperature superconductors. |
| first_indexed | 2024-12-24T01:01:30Z |
| format | Article |
| id | doaj.art-c25d0db147d04280aefda86430a4ab02 |
| institution | Directory Open Access Journal |
| issn | 2057-3960 |
| language | English |
| last_indexed | 2024-12-24T01:01:30Z |
| publishDate | 2022-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Computational Materials |
| spelling | doaj.art-c25d0db147d04280aefda86430a4ab022022-12-21T17:23:21ZengNature Portfolionpj Computational Materials2057-39602022-01-01811810.1038/s41524-021-00666-7Machine learning of superconducting critical temperature from Eliashberg theoryS. R. Xie0Y. Quan1A. C. Hire2B. Deng3J. M. DeStefano4I. Salinas5U. S. Shah6L. Fanfarillo7J. Lim8J. Kim9G. R. Stewart10J. J. Hamlin11P. J. Hirschfeld12R. G. Hennig13Department of Materials Science and Engineering, University of FloridaDepartment of Materials Science and Engineering, University of FloridaDepartment of Materials Science and Engineering, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Physics, University of FloridaDepartment of Materials Science and Engineering, University of FloridaAbstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c. McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α 2 F(ω). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α 2 F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α 2 F functions and numerical solutions of the Eliashberg equations, we derive a formula for T c that performs as well as Allen–Dynes for low-T c superconductors and substantially better for higher-T c ones. This corrects the systematic underestimation of T c while reproducing the physical constraints originally outlined by Allen and Dynes. This equation should replace the Allen–Dynes formula for the prediction of higher-temperature superconductors.https://doi.org/10.1038/s41524-021-00666-7 |
| spellingShingle | 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 R. G. Hennig Machine learning of superconducting critical temperature from Eliashberg theory npj Computational Materials |
| title | Machine learning of superconducting critical temperature from Eliashberg theory |
| title_full | Machine learning of superconducting critical temperature from Eliashberg theory |
| title_fullStr | Machine learning of superconducting critical temperature from Eliashberg theory |
| title_full_unstemmed | Machine learning of superconducting critical temperature from Eliashberg theory |
| title_short | Machine learning of superconducting critical temperature from Eliashberg theory |
| title_sort | machine learning of superconducting critical temperature from eliashberg theory |
| url | https://doi.org/10.1038/s41524-021-00666-7 |
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