Correlation stabilized anomalous Hall crystal in bilayer graphene

Correlation stabilized anomalous Hall crystal in 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 Correlation stabilized anomalous Hall crystal in bilayer graphene Jianpeng Liu, Zhongqing Guo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5855283/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract When the charge density is sufficiently low, interacting two-dimensional electron gas (2DEG) would undergo a phase transition from homogeneous Fermi liquid to an electronic crystal state, known as Wigner crystal. Besides conventional 2DEG, various topological fermionic excitations may also be realized in 2D materials. For example, ``high-order" Dirac fermions exhibiting nontrivial Berry phases may approximately characterize the low-energy excitations in rhombohedral multilayer graphene (RMG). In this work, we develop a beyond-mean-field theoretical framework to study the interacting ground states and single-particle excitations in slightly charge-doped RMG under vertical electric field. We find that transitions from Fermi liquid to trivial Wigner-crystal states would occur at critical carrier density $\sim 10^{10},\textrm{cm}^{-2}$ for all $n$-layer RMG (with $n=2, 3, 4, 5, 6$) which are approximately described by $n$-order Dirac-fermion models. Most saliently, using a more realistic modeling of bilayer graphene including trigonal warping effects, we find that an anomalous Hall crystal state with spontaneous quantized anomalous Hall conductivity would emerge when the carrier density is below $\sim 1\times 10^{11},\text{cm}^{-2}$, and it becomes the unique ground state over trivial Wigner crystal when the density is further lower. Counter intuitively, such topological anomalous Hall crystal becomes more stable than the trivial Wigner crystal due to the lower correlation energy gained from dynamical charge fluctuations, which is beyond mean-field description. Our work suggests that slightly carrier-doped bilayer graphene is one of the most promising candidates to realize anomalous Hall crystal. Moreover, the method developed in this work can be readily applied to other interacting 2D systems including moir'e superlattices. Physical sciences/Physics/Condensed-matter physics/Topological matter Physical sciences/Physics/Condensed-matter physics/Quantum fluids and solids Full Text Additional Declarations There is NO Competing Interest. Supplementary Files codes.zip Codes for GW+RPA calculations suppv2.pdf Correlation stabilized anomalous Hall crystal in bilayer graphene Cite Share Download PDF Status: Published Journal Publication published 13 Dec, 2025 Read the published version in Nature Communications → 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-5855283","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":416256810,"identity":"cfc8ee13-742b-4266-a77f-e37a5fa65c81","order_by":0,"name":"Jianpeng Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYBACPmYGBgOGCoYEIJsNxGRgkABiHjxa2MBazsC1GBChBUQwtsG0MBCjhZ3HoLhwXl0e/+z2aw9+FPyR45/dwPjgbRuDvDlOh/EYGM/cdrhY4s6ZcsMeAwNjiTsHmA3ntjEY7mzAo4V324HEhhs5aRI8BgaJGyQS2KR5gU41OIBPy5y6xPlALZJ/DAzqgVrYfxPW0sCcuOFG+jFpoC0JBkBbmPFrYSswnnHscOLGGzls0jIGxoYzbiQ2S845J2G4AYcWfv7D24wLauoS591Ifyb55o+cPP+M5IMf3pTZyOOyBWSRMYTmMYAKMDYwQGIHJ2B+DKHZH+BTNQpGwSgYBSMYAADeylJ0AMFUfgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-8564-0415","institution":"ShanghaiTech University","correspondingAuthor":true,"prefix":"","firstName":"Jianpeng","middleName":"","lastName":"Liu","suffix":""},{"id":416256811,"identity":"86d29a3e-02fd-4b09-8493-8063157d5c32","order_by":1,"name":"Zhongqing Guo","email":"","orcid":"","institution":"School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China","correspondingAuthor":false,"prefix":"","firstName":"Zhongqing","middleName":"","lastName":"Guo","suffix":""}],"badges":[],"createdAt":"2025-01-18 13:10:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5855283/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5855283/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-66179-9","type":"published","date":"2025-12-13T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98856950,"identity":"396e1f64-6ae2-4aeb-b0b3-98bb63ea6eb9","added_by":"auto","created_at":"2025-12-23 08:05:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2291948,"visible":true,"origin":"","legend":"Article File","description":"","filename":"manuscriptNC2.3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5855283/v1_covered_4963dbf9-fb77-4320-8c52-1e9d622b0a43.pdf"},{"id":76624718,"identity":"de2bf72c-8346-4cf6-ae9d-f7a655138083","added_by":"auto","created_at":"2025-02-19 05:31:04","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":24096,"visible":true,"origin":"","legend":"Codes for GW+RPA calculations","description":"","filename":"codes.zip","url":"https://assets-eu.researchsquare.com/files/rs-5855283/v1/811923094e5804671f207a89.zip"},{"id":76624715,"identity":"4b38be10-6e3b-4c54-a07d-c78ba7da98f7","added_by":"auto","created_at":"2025-02-19 05:31:02","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":4801311,"visible":true,"origin":"","legend":"Correlation stabilized anomalous Hall crystal in bilayer graphene","description":"","filename":"suppv2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5855283/v1/bab9f1229035cb978c4360b0.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Correlation stabilized anomalous Hall crystal in bilayer graphene","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-5855283/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5855283/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"When the charge density is sufficiently low, interacting two-dimensional electron gas (2DEG) would undergo a phase transition from homogeneous Fermi liquid to an electronic crystal state, known as Wigner crystal. Besides conventional 2DEG, various topological fermionic excitations may also be realized in 2D materials. For example, ``high-order\" Dirac fermions exhibiting nontrivial Berry phases may approximately characterize the low-energy excitations in rhombohedral multilayer graphene (RMG). In this work, we develop a beyond-mean-field theoretical framework to study the interacting ground states and single-particle excitations in slightly charge-doped RMG under vertical electric field. We find that transitions from Fermi liquid to trivial Wigner-crystal states would occur at critical carrier density $\\sim 10^{10}\\,\\textrm{cm}^{-2}$ for all $n$-layer RMG (with $n=2, 3, 4, 5, 6$) which are approximately described by $n$-order Dirac-fermion models. Most saliently, using a more realistic modeling of bilayer graphene including trigonal warping effects, we find that an anomalous Hall crystal state with spontaneous quantized anomalous Hall conductivity would emerge when the carrier density is below $\\sim 1\\times 10^{11}\\,\\text{cm}^{-2}$, and it becomes the unique ground state over trivial Wigner crystal when the density is further lower. Counter intuitively, such topological anomalous Hall crystal becomes more stable than the trivial Wigner crystal due to the lower correlation energy gained from dynamical charge fluctuations, which is beyond mean-field description. Our work suggests that slightly carrier-doped bilayer graphene is one of the most promising candidates to realize anomalous Hall crystal. Moreover, the method developed in this work can be readily applied to other interacting 2D systems including moir\\'e superlattices.","manuscriptTitle":"Correlation stabilized anomalous Hall crystal in bilayer graphene","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-19 05:30:54","doi":"10.21203/rs.3.rs-5855283/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"50144ef9-62df-4775-ad82-61a50d55ffa7","owner":[],"postedDate":"February 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":44387338,"name":"Physical sciences/Physics/Condensed-matter physics/Topological matter"},{"id":44387339,"name":"Physical sciences/Physics/Condensed-matter physics/Quantum fluids and solids"}],"tags":[],"updatedAt":"2025-12-23T08:05:44+00:00","versionOfRecord":{"articleIdentity":"rs-5855283","link":"https://doi.org/10.1038/s41467-025-66179-9","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-12-13 05:00:00","publishedOnDateReadable":"December 13th, 2025"},"versionCreatedAt":"2025-02-19 05:30:54","video":"","vorDoi":"10.1038/s41467-025-66179-9","vorDoiUrl":"https://doi.org/10.1038/s41467-025-66179-9","workflowStages":[]},"version":"v1","identity":"rs-5855283","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5855283","identity":"rs-5855283","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}