Anomalous coherence length in superconductors with quantum metric

Abstract The coherence length ξ is the fundamental length scale of superconductors which governs the sizes of Cooper pairs, vortices, Andreev bound states, and more. In BCS theory, the coherence length is ξ BCS = ℏ v F /Δ, where v F is the Fermi velocity and Δ is the pairing gap. It is clear that in...

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Main Authors: Jin-Xin Hu, Shuai A. Chen, K. T. Law
Format: Article
Language:English
Published: Nature Portfolio 2025-01-01
Series:Communications Physics
Online Access:https://doi.org/10.1038/s42005-024-01930-0
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author Jin-Xin Hu
Shuai A. Chen
K. T. Law
author_facet Jin-Xin Hu
Shuai A. Chen
K. T. Law
author_sort Jin-Xin Hu
collection DOAJ
description Abstract The coherence length ξ is the fundamental length scale of superconductors which governs the sizes of Cooper pairs, vortices, Andreev bound states, and more. In BCS theory, the coherence length is ξ BCS = ℏ v F /Δ, where v F is the Fermi velocity and Δ is the pairing gap. It is clear that increasing Δ will shorten ξ BCS. In this work, we show that the quantum metric, which is the real part of the quantum geometric tensor, gives rise to an anomalous contribution to the coherence length. Specifically, $$\xi =\sqrt{{\xi }_{{{{\rm{BCS}}}}}^{2}+{\ell }_{{{{\rm{qm}}}}}^{2}}$$ ξ = ξ BCS 2 + ℓ qm 2 for a superconductor where ℓ qm is the quantum metric contribution. In the flat-band limit, ξ does not vanish but is bound below by ℓ qm. We demonstrate that under the uniform pairing condition, ℓ qm is controlled by the quantum metric of minimal trace in the flat-band limit. Physically, the Cooper pair size of a superconductor cannot be squeezed down to a size smaller than ℓ qm which is a fundamental length scale determined by the quantum geometry of the wave functions. Lastly, we compute the quantum metric contributions for the family of superconducting moiré graphene materials, demonstrating the significant role played by quantum metric effects in these narrow-band superconductors.
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spelling doaj-art-08ff986bbb704ead94b0c161420a243e2025-01-19T12:26:22ZengNature PortfolioCommunications Physics2399-36502025-01-01811710.1038/s42005-024-01930-0Anomalous coherence length in superconductors with quantum metricJin-Xin Hu0Shuai A. Chen1K. T. Law2Department of Physics, Hong Kong University of Science and TechnologyDepartment of Physics, Hong Kong University of Science and TechnologyDepartment of Physics, Hong Kong University of Science and TechnologyAbstract The coherence length ξ is the fundamental length scale of superconductors which governs the sizes of Cooper pairs, vortices, Andreev bound states, and more. In BCS theory, the coherence length is ξ BCS = ℏ v F /Δ, where v F is the Fermi velocity and Δ is the pairing gap. It is clear that increasing Δ will shorten ξ BCS. In this work, we show that the quantum metric, which is the real part of the quantum geometric tensor, gives rise to an anomalous contribution to the coherence length. Specifically, $$\xi =\sqrt{{\xi }_{{{{\rm{BCS}}}}}^{2}+{\ell }_{{{{\rm{qm}}}}}^{2}}$$ ξ = ξ BCS 2 + ℓ qm 2 for a superconductor where ℓ qm is the quantum metric contribution. In the flat-band limit, ξ does not vanish but is bound below by ℓ qm. We demonstrate that under the uniform pairing condition, ℓ qm is controlled by the quantum metric of minimal trace in the flat-band limit. Physically, the Cooper pair size of a superconductor cannot be squeezed down to a size smaller than ℓ qm which is a fundamental length scale determined by the quantum geometry of the wave functions. Lastly, we compute the quantum metric contributions for the family of superconducting moiré graphene materials, demonstrating the significant role played by quantum metric effects in these narrow-band superconductors.https://doi.org/10.1038/s42005-024-01930-0
spellingShingle Jin-Xin Hu
Shuai A. Chen
K. T. Law
Anomalous coherence length in superconductors with quantum metric
Communications Physics
title Anomalous coherence length in superconductors with quantum metric
title_full Anomalous coherence length in superconductors with quantum metric
title_fullStr Anomalous coherence length in superconductors with quantum metric
title_full_unstemmed Anomalous coherence length in superconductors with quantum metric
title_short Anomalous coherence length in superconductors with quantum metric
title_sort anomalous coherence length in superconductors with quantum metric
url https://doi.org/10.1038/s42005-024-01930-0
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AT shuaiachen anomalouscoherencelengthinsuperconductorswithquantummetric
AT ktlaw anomalouscoherencelengthinsuperconductorswithquantummetric