Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Intervalley Coherent Phase

Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Intervalley Coherent Phase | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Intervalley Coherent Phase Shuai Chen, Chun Wang Chau, Kam Tuen Law This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6201818/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Superconductivity (SC) is observed in rhombohedral trilayer graphene (RTG) in a narrow regime between the flavor-symmetric state and the symmetry breaking phase, which cannot be described by the conventional BCS theory. The measured coherence length, for instance, is roughly two orders of magnitude shorter than the value predicted by the BCS relation based on the large fermi velocity and an extremely low charge carrier densities of the flavor-symmetric phase. To resolve the discrepancies, we propose that the RTG SC phase arises from the pairing of quasiparticles of the adjacent inter-valley coherent (IVC) state. We illustrate the SC behavior using gapped Dirac cones with the chemical potential $\mu$ close to the conduction band's bottom. Our findings indicate that the transition temperature $T_c$ obeys $T_c\propto \epsilon_D\exp(-2/\rho_\mathrm{qp}U)$ with the density of states $\rho_\mathrm{qp}$ of IVC quasiparticles, which is much suppressed compared to predictions from the BCS theory. The coherence length $\xi$ we predict behaves according to $\xi\sim v/\sqrt{\mu T_c }$ with $v$ being the velocity of Dirac cone. Applying our assumption to a microscopic model, our predictions align well with experimental data and effectively capture key measurable quantities such as the transition temperature $T_c$ and the coherence length $\xi$ without parameter fine-tuning. Physical sciences/Physics/Condensed-matter physics/Superconducting properties and materials Physical sciences/Physics/Condensed-matter physics/Electronic properties and materials Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6201818","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":440176397,"identity":"fa0c1ee2-17c3-4a85-8b25-934a552433f8","order_by":0,"name":"Shuai Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAk0lEQVRIiWNgGAWjYDACCQY2hg9gBhsJWhhngCiStDDzkKSFf3b7s8e2bXV1DNJtCURacueMuXFu22EJBpljB4jTYiCRwyad23YA6LD0BmK1pD+TtmyrI0lLgpk0YxszUEsakQ6TuJFjJtlz7rBkm0RaAnFa+GekP5P4UVbHzy+RZkCcFjggOiJHwSgYBaNgFBABAK1FIlzOF9f9AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-8996-7503","institution":"Hong Kong University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Shuai","middleName":"","lastName":"Chen","suffix":""},{"id":440176398,"identity":"263f27cf-2c6b-413e-b984-2df67ef69bc4","order_by":1,"name":"Chun Wang Chau","email":"","orcid":"https://orcid.org/0009-0000-8246-9053","institution":"Hong Kong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Chun","middleName":"Wang","lastName":"Chau","suffix":""},{"id":440176399,"identity":"b5a94412-f87a-47fd-8248-5a74b7cf124d","order_by":2,"name":"Kam Tuen Law","email":"","orcid":"https://orcid.org/0000-0003-0501-6290","institution":"The Hong Kong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Kam","middleName":"Tuen","lastName":"Law","suffix":""}],"badges":[],"createdAt":"2025-03-11 09:50:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6201818/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6201818/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96252516,"identity":"bc25e1b7-47ba-4b01-bcbf-bd607eee008f","added_by":"auto","created_at":"2025-11-19 07:41:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2296838,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6201818/v1_covered_79ece3ee-db4a-46e9-a2f6-43e7d4b3b23a.pdf"},{"id":96195015,"identity":"47d60e4a-1889-4bfc-a366-07703f85dd79","added_by":"auto","created_at":"2025-11-18 15:20:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2296838,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6201818/v1_covered_83ced09f-b131-424f-9f78-bb055c9509c1.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Intervalley Coherent Phase","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6201818/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6201818/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSuperconductivity (SC) is observed in rhombohedral trilayer graphene (RTG) in a narrow regime between the flavor-symmetric state and the symmetry breaking phase, which cannot be described by the conventional BCS theory. The measured coherence length, for instance, is roughly two orders of magnitude shorter than the value predicted by the BCS relation based on the large fermi velocity and an extremely low charge carrier densities of the flavor-symmetric phase. To resolve the discrepancies, we propose that the RTG SC phase arises from the pairing of quasiparticles of the adjacent inter-valley coherent (IVC) state. We illustrate the SC behavior using gapped Dirac cones with the chemical potential $\\mu$ close to the conduction band's bottom. Our findings indicate that the transition temperature $T_c$ obeys $T_c\\propto \\epsilon_D\\exp(-2/\\rho_\\mathrm{qp}U)$ with the density of states $\\rho_\\mathrm{qp}$ of IVC quasiparticles, which is much suppressed compared to predictions from the BCS theory. The coherence length $\\xi$ we predict behaves according to $\\xi\\sim v/\\sqrt{\\mu T_c }$ with $v$ being the velocity of Dirac cone. 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