Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?
Abstract
Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.
Additional Information
© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received 19 February 2021; Accepted 24 August 2021; Published 30 September 2021. We thank Jason Alicea, Erez Berg, Johannes Hofmann, and Pablo Jarillo-Herrero for useful discussions and Jonathan Ruhman for an earlier collaboration. C.L. acknowledges support from the Gordon and Betty Moore Foundation through Grant GBMF8682. S.N-P. acknowledges support from NSF (DMR-1753306), the Sloan Foundation, and the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250. D.C. is supported by a faculty startup grant at Cornell University. Data availability: The data that support the findings of this study are available from the corresponding author upon reasonable request. Code availability: The code that supports the findings of this study is available from the corresponding author upon reasonable request. Author Contributions: C.L. and D.C. designed research. C.L. performed numerical calculations (supervised by D.C.). S.N.-P. provided experimental inputs for the HF calculations. C.L, S.N.-P., and D.C. analyzed results. C.L. and D.C. wrote the paper with input from S.N.-P. The authors declare no competing interests.Attached Files
Published - s41535-021-00379-6.pdf
Submitted - 2102.05661.pdf
Supplemental Material - 41535_2021_379_MOESM1_ESM.pdf
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Additional details
- Eprint ID
- 108448
- Resolver ID
- CaltechAUTHORS:20210316-084002156
- GBMF8682
- Gordon and Betty Moore Foundation
- DMR-1753306
- NSF
- Alfred P. Sloan Foundation
- Institute for Quantum Information and Matter (IQIM)
- GBMF1250
- Gordon and Betty Moore Foundation
- Cornell University
- Created
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2021-03-19Created from EPrint's datestamp field
- Updated
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2023-03-15Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter