Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C > 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene

Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C > 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene | 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 Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C > 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene Võ Tiến Phong, Cyprian Lewandowski This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6978415/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 Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moir\'{e} materials when a topologically nontrivial band with Chern number C=1 is partially doped. Remarkably, superlattice Bloch bands can carry higher Chern numbers that defy the Landau-level paradigm and may even host exotic fractionalized states with non-Abelian quasiparticles. Inspired by this exciting possibility, we propose twisted \textit{rhombohedral} trilayer-bilayer graphene at $\theta \sim 1.2^\circ$ as a field-tunable quantum anomalous Chern insulator that features spectrally-isolated, kinetically-quenched, and topologically-nontrivial bands with $\mathcal{C} = 2,3$ favorable for fractional phases once fractionally doped, as characterized by their quantum geometry. Based on extensive self-consistent mean-field calculations, we show that these phases are stabilized by Coulomb interactions and are robust against variations in dielectric environment, tight-binding hopping parameters, and lattice relaxation. Physical sciences/Physics/Condensed-matter physics/Quantum Hall Physical sciences/Physics/Condensed-matter physics/Electronic properties and materials Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological insulators Full Text Additional Declarations There is NO Competing Interest. Supplementary Files NatPhysSI.pdf Supplementary Material 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-6978415","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":485770758,"identity":"abb44582-fae5-4bb8-a6e7-68975dd7dfaf","order_by":0,"name":"Võ Tiến Phong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYHACNhAhB+Pxg0keIrQYQ9gJDJINxGpJbCBai8Hx3mMPPu6oTV/bfvzag48/GCTkZyQwPnjbhkfLmXPphjPPHM/ddian3HBGAoOEwY0EZsO5eLRIzsgxk+ZtO5a77UBOmjRPAkOdgUQCG1CEsJZ0s/Nv0qT/JIAdxv4bnxZ+CbCWmgSzG+nHpIHel2C4kcDGjFcLz7k0yZltBwy33XjDJtmTJiFhcOZhs+Scc7i1sLH3HpP42FYnb3Y+/ZnEDxsbCfn25IMf3pTh1gKNgsMghgGQkABixgZ86mFa6oCY/QEBlaNgFIyCUTBSAQAg/E/1/Mbq1AAAAABJRU5ErkJggg==","orcid":"","institution":"Florida State University","correspondingAuthor":true,"prefix":"","firstName":"Võ","middleName":"Tiến","lastName":"Phong","suffix":""},{"id":485770759,"identity":"7d84dce3-b7f0-4e1e-aadd-106386793446","order_by":1,"name":"Cyprian Lewandowski","email":"","orcid":"https://orcid.org/0000-0002-6944-9805","institution":"Florida State University","correspondingAuthor":false,"prefix":"","firstName":"Cyprian","middleName":"","lastName":"Lewandowski","suffix":""}],"badges":[],"createdAt":"2025-06-26 01:05:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6978415/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6978415/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90060637,"identity":"737a4176-b573-47a4-b296-4d8f40e981bb","added_by":"auto","created_at":"2025-08-28 03:22:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11115210,"visible":true,"origin":"","legend":"Article File","description":"","filename":"NatPhysmain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6978415/v1_covered_76d43fee-640c-4ffc-b50e-efa821f94325.pdf"},{"id":90060149,"identity":"14caf35b-eb26-4fc6-a02c-260d4f3e2b28","added_by":"auto","created_at":"2025-08-28 03:14:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":52413075,"visible":true,"origin":"","legend":"Supplementary Material","description":"","filename":"NatPhysSI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6978415/v1/3c4b9aeabd3ab0f024c9c7fb.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eCoulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C \u0026gt; 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"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-6978415/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6978415/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moir\\'{e} materials when a topologically nontrivial band with Chern number C=1 is partially doped. Remarkably, superlattice Bloch bands can carry higher Chern numbers that defy the Landau-level paradigm and may even host exotic fractionalized states with non-Abelian quasiparticles. Inspired by this exciting possibility, we propose twisted \\textit{rhombohedral} trilayer-bilayer graphene at $\\theta \\sim 1.2^\\circ$ as a field-tunable quantum anomalous Chern insulator that features spectrally-isolated, kinetically-quenched, and topologically-nontrivial bands with $\\mathcal{C} = 2,3$ favorable for fractional phases once fractionally doped, as characterized by their quantum geometry. 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