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Accelerating the calculation of electron–phonon coupling strength with machine learning

Nature Computational Science volume 4, pages 615–625 (2024)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

The calculation of electron–phonon couplings (EPCs) is essential for understanding various fundamental physical properties, including electrical transport, optical and superconducting behaviors in materials. However, obtaining EPCs through fully first-principles methods is notably challenging, particularly for large systems or when employing advanced functionals. Here we introduce a machine learning framework to accelerate EPC calculations by utilizing atomic orbital-based Hamiltonian matrices and gradients predicted by an equivariant graph neural network. We demonstrate that our method not only yields EPC values in close agreement with first-principles results but also enhances calculation efficiency by several orders of magnitude. Application to GaAs using the Heyd–Scuseria–Ernzerhof functional reveals the necessity of advanced functionals for accurate carrier mobility predictions, while for the large Kagome crystal CsV3Sb5, our framework reproduces the experimentally observed double domes in pressure-induced superconducting phase diagrams. This machine learning framework offers a powerful and efficient tool for the investigation of diverse EPC-related phenomena in complex materials.

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Fig. 1: Efficient construction of Hamiltonian matrices and electron–phonon interaction framework using HamGNN.
Fig. 2: Comparison of EPC matrix elements.
Fig. 3: Band structures, mobility convergence and scattering rates of GaAs.
Fig. 4: Crystal structure, Kagome lattice and superconducting transition temperature (Tc) of CsV3Sb5.
Fig. 5: Energy bands, phonon spectrum and atomic vibration modes in the CDW phase of CsV3Sb5.

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Data availability

The Hamiltonian and Hamiltonian gradient data, generated by HamGNN, are available on Zenodo at https://doi.org/10.5281/zenodo.11204268 (ref. 45) for calculating the carrier mobility of GaAs and the superconducting transition temperature of CsV3Sb5. Source data are provided with this paper.

Code availability

The code for calculating the mobility and superconductivity is available on GitHub (https://github.com/QuantumLab-ZY/HamEPC) and Zenodo at https://doi.org/10.5281/zenodo.12685941 (ref. 46).

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Acknowledgements

We would like to express our gratitude to H. Shang and X. Qin for their valuable online discussions on the EPC and use of HONPAS. We acknowledge financial support from the Ministry of Science and Technology of the People’s Republic of China (no. 2022YFA1402901, H.X.), NSFC (grant nos. 11991061, X.-G.G. and 12188101, H.X.), the Guangdong Major Project of the Basic and Applied Basic Research (Future functional materials under extreme conditions—2021B0301030005, H.X.), the Shanghai Science and Technology Program (no. 23JC1400900, H.X.) and the Shanghai Pilot Program for Basic Research – Fudan University 21TQ1400100 (no. 22TQ017, W.C.).

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  1. These authors contributed equally: Yang Zhong, Shixu Liu.

Authors and Affiliations

  1. Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, China

    Yang Zhong, Shixu Liu, Binhua Zhang, Zhiguo Tao, Yuting Sun, Weibin Chu, Xin-Gao Gong, Ji-Hui Yang & Hongjun Xiang

  2. Shanghai Qi Zhi Institute, Shanghai, China

    Yang Zhong, Shixu Liu, Binhua Zhang, Zhiguo Tao, Yuting Sun, Weibin Chu, Xin-Gao Gong, Ji-Hui Yang & Hongjun Xiang

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Contributions

H.X. and J.-H.Y. proposed the research and the methodology in this work. Y.Z. and S.L. wrote the codes, performed the EPC calculation and wrote the paper. B.Z. conducted structure relaxation and phonon calculations for CsV3Sb5. Z.T, Y.S. and W.C. checked the formulas and codes. H.X., J.-H.Y. and X.-G.G. revised the paper. All authors discussed the results.

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Correspondence to Ji-Hui Yang or Hongjun Xiang.

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Nature Computational Science thanks Ting Cao, Yuan Ping and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Zhong, Y., Liu, S., Zhang, B. et al. Accelerating the calculation of electron–phonon coupling strength with machine learning. Nat Comput Sci 4, 615–625 (2024). https://doi.org/10.1038/s43588-024-00668-7

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