Stephen Xie^1,2*, Yundi Quan^1,2,3, Ajinkya Hire^1,2, Boning Deng³, Jonathan DeStefano³, Ian Salinas³, Urja Shah³, Laura Fanfarillo³, Jinhyuk Lim³, Jungsoo Kim³, Gregory Stewart³, James Hamlin³, Peter Hirschfeld³, Richard Hennig^1,2

1 Department of Materials Science and Engineering, University of Florida, USA

2 Quantum Theory Project, University of Florida, USA

3 Department of Physics, University of Florida, USA

* Corresponding authors emails: sxiexie@gmail.com

DOI10.24435/materialscloud:68-6p [version v1]

Publication date: Sep 18, 2021

How to cite this record

Stephen Xie, Yundi Quan, Ajinkya Hire, Boning Deng, Jonathan DeStefano, Ian Salinas, Urja Shah, Laura Fanfarillo, Jinhyuk Lim, Jungsoo Kim, Gregory Stewart, James Hamlin, Peter Hirschfeld, Richard Hennig, Machine learning of superconducting critical temperature from Eliashberg theory, Materials Cloud Archive 2021.150 (2021), https://doi.org/10.24435/materialscloud:68-6p

Description

The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional electron-phonon superconductors, including the retardation of the interaction and the effect of the Coulomb pseudopotential, to predict the critical temperature Tc and other properties. McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature predicted by this theory, which depends essentially on the electron-phonon spectral function α²F(ω), using α²F for low-Tc superconductors. Here we show that modern machine learning techniques can substantially improve these formulae, accounting for more general shapes of the α²F function. Using symbolic regression and the sure independence screening and sparsifying operator (SISSO) framework, together with a database of artificially generated α²F functions, ranging from multimodal Einstein-like models to calculated spectra of polyhydrides, as well as numerical solutions of the Eliashberg equations, we derive a formula for Tc that performs as well as Allen-Dynes for low-Tc superconductors and substantially better for higher-Tc ones. The expression identified through our data-driven approach corrects the systematic underestimation of Tc 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 and the estimation of λ from experimental data. This repository contains CSV tables of model inputs, prefactors, and critical temperature predictions used for machine learning and validation in this work. Additionally, the inputs and outputs of the SISSO framework for both rounds of symbolic regression are included. Please see https://github.com/henniggroup/symbolic-regression-utilities for tools to create and analyze SISSO inputs and outputs.

Materials Cloud sections using this data

Files

File name	Size	Description
data_tables.zip MD5md5:86c68504d1780b6fc7eaccbd4116706c	419.0 KiB	Data tables including model inputs, prefactors, and critical temperature predictions. Data is partitioned by data source: Allen-Dynes 1975, Gaussian-based artificial, EPW-calculated, literature, and hydrides.
sisso_runs.zip MD5md5:80c0ecb90d72b6dbb31dbeb82c10e0ab	7.4 MiB	Inputs and outputs of the SISSO framework for both rounds of symbolic regression. Please see https://github.com/henniggroup/symbolic-regression-utilities for tools to create and analyze SISSO inputs and outputs.

License

Files and data are licensed under the terms of the following license: Apache License 2.0.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Keywords

supercondcutivity symbolic regression machine learning