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Non-trivial quantum geometry and the strength of electron–phonon coupling

Nature Physics volume 20, pages 1262–1268 (2024)Cite this article

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Abstract

Electron–phonon coupling is crucial for the existence of various phases of matter, in particular superconductivity and density waves. Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron–phonon coupling, demonstrating the crucial contributions of the Fubini–Study metric or its orbital selective version to the dimensionless electron–phonon coupling constant. We apply the theory to two materials, that is, graphene and MgB2, where the geometric contributions account for approximately 50% and 90% of the total electron–phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions. Our results suggest that the non-trivial electron band geometry or topology might favour superconductivity with a relatively high critical temperature.

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Fig. 1: Quantum geometry and EPC.
Fig. 2: Plots for graphene.
Fig. 3: Plots for MgB2.

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Data availability

The datasets generated during and/or analysed during the current study are available from the authors on reasonable request. Source data are provided with this paper.

Code availability

The code generated during and/or analysed for the current study is available from the authors on reasonable request.

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Acknowledgements

We acknowledge E. Baldini, D. Calugaru, M. Cheng, S. Das Sarma, L. Glazman, F. D. M. Haldane, J. Herzog-Arbeitman, H. Hu, L.-H. Hu, Y. H. Kwan, B. Lian, C. -Hwan Park, Z.-D. Song, I. Souza, J. Sous, X.-Q. Sun, P. Törmä, Y. Xu, R.-X. Zhang and especially C.-X. Liu for helpful discussion. B.A.B.’s research was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 101020833) and partially by the Simons Investigator grant no. 404513, the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme, the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant no. GBMF11070), the Office of Naval Research (grant no. N00014-20-1-2303), the Global Collaborative Network Grant at Princeton University, the BSF Israel–US Foundation (no. 2018226) and the NSF-MERSEC (grant no. MERSEC DMR 2011750). J.Y. is supported by the Gordon and Betty Moore Foundation through grant no. GBMF8685 toward the Princeton theory programme. I.E. and B.A.B. are part of the SuperC collaboration. I.E. has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 802533) and the Department of Education, Universities and Research of the Eusko Jaurlaritza and the University of the Basque Country UPV/EHU (grant no. IT1527-22). Calculations by C.J.C. and P.N. were supported by Office of Naval Research grant no. 13672292 and by Gordon and Betty Moore Foundation grant no. 8048. P.N. gratefully acknowledges support from the Alexander von Humboldt Foundation (Bessel Research Award) and from the John Simon Guggenheim Memorial Foundation (Guggenheim Fellowship).

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Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, USA

    Jiabin Yu & B. Andrei Bernevig

  2. Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD, USA

    Jiabin Yu

  3. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    Christopher J. Ciccarino

  4. College of Letters and Science, University of California, Los Angeles, CA, USA

    Christopher J. Ciccarino & Prineha Narang

  5. Centro de Física de Materiales (CSIC-UPV/EHU), Donostia/San Sebastián, Spain

    Raffaello Bianco & Ion Errea

  6. Ruder Bosković Institute, Zagreb, Croatia

    Raffaello Bianco

  7. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Modena, Italy

    Raffaello Bianco

  8. Centro S3, Istituto Nanoscienze-CNR, Modena, Italy

    Raffaello Bianco

  9. Fisika Aplikatua Saila, Gipuzkoako Ingeniaritza Eskola, University of the Basque Country (UPV/EHU), Donostia/San Sebastián, Spain

    Ion Errea

  10. Donostia International Physics Center, Donostia/San Sebastián, Spain

    Ion Errea & B. Andrei Bernevig

  11. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    B. Andrei Bernevig

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  1. Jiabin Yu
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  2. Christopher J. Ciccarino
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Contributions

J.Y. and B.A.B. conceived and supervised the project. J.Y. and B.A.B. performed the theoretical analysis. C.J.C., R.B., I.E. and P.N. performed the ab initio calculations. J.Y. and B.A.B. wrote the paper, with input from C.J.C., R.B., I.E. and P.N.

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Correspondence to B. Andrei Bernevig.

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Supplementary Figs. 1–10, Discussion and Tables I and II.

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Data obtained from numerical calculations for Fig. 2.

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Yu, J., Ciccarino, C.J., Bianco, R. et al. Non-trivial quantum geometry and the strength of electron–phonon coupling. Nat. Phys. 20, 1262–1268 (2024). https://doi.org/10.1038/s41567-024-02486-0

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