Unified microscopic theory of integer and fractional quantum Hall effects

Unified microscopic theory of integer and fractional quantum Hall effects | 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 Physical Sciences - Article Unified microscopic theory of integer and fractional quantum Hall effects Pedro Pereyra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8689913/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We demonstrate that the integer and fractional quantum Hall effects originate from a common microscopic mechanism: boundary-induced quantization of edge states in confined two-dimensional electron systems. Although integer and fractional Hall plateaus are traditionally described using distinct theoretical frameworks, their universal coexistence in finite samples has lacked a unified microscopic explanation. Here we show that this missing link is provided by the quantization of edge states by physically consistent boundary conditions. Starting from the Landau problem in finite geometries, we show that Dirichlet, Neumann, and mixed (Robin) boundary conditions discretize the guiding-center coordinate and the longitudinal momentum of edge states, generating families of chiral edge channels with boundary-dependent multiplicities. When incorporated into the Landauer–Büttiker transport formalism, these multiplicities naturally produce the integer Hall plateaus and a structured hierarchy of fractional filling factors. We further show that retaining a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum without modifying the bulk Landau levels, enabling the strong-field fractional plateaus observed experimentally. Boundary quantization, refined by weak parity breaking, produces a fine structure of edge energies in which selected chiral branches remain pinned to the Fermi level, providing a unified microscopic foundation for quantized Hall transport across both integer and fractional regimes. Physical sciences/Physics/Condensed-matter physics/Quantum Hall Physical sciences/Physics/Quantum physics/Quantum mechanics Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted 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. 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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-8689913","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":580396356,"identity":"e9aa70aa-8f20-4ca0-9ee4-352e5a72d2e2","order_by":0,"name":"Pedro Pereyra","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYDADftK1SDaQrMXgALEqzaWbj3342HZP3vj48YcfGNvsohnEzhjg1WI551jyzJltxYbbziQkSzC2Jec2SKcl4HfPjRxjZt62BMZtBxKOMTC2MQO1JON3o8GN/M/Mf9sS7Df3P2wDaqkHaklsIGQLMzNjW0LiBolkNqCWw4RtAfrFmLHnXELyjBvPmCUSzh3PbSPkF2CIPWb4UZZg29+f/vDDh7Lq3H7pHPwhZiABJBjZoDyQ8Wy4FSNpYfhDSNkoGAWjYBSMaAAAFhRGFXdCQYIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-9660-1756","institution":"Universidad Autónoma Metropolitana campus Azcapotzalco","correspondingAuthor":true,"prefix":"","firstName":"Pedro","middleName":"","lastName":"Pereyra","suffix":""}],"badges":[],"createdAt":"2026-01-25 03:30:11","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8689913/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8689913/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101752224,"identity":"1ff27f7e-53c3-45ad-9e04-3a4cc4f53607","added_by":"auto","created_at":"2026-02-03 10:26:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1463963,"visible":true,"origin":"","legend":"Article File","description":"","filename":"QHEPPereyraNature24JL.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8689913/v1_covered_aeafb2ee-0f4b-427f-9749-e1452bf85d7d.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Unified microscopic theory of integer and fractional quantum Hall effects","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8689913/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8689913/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We demonstrate that the integer and fractional quantum Hall effects originate from a common microscopic mechanism: boundary-induced quantization of edge states in confined two-dimensional electron systems. Although integer and fractional Hall plateaus are traditionally described using distinct theoretical frameworks, their universal coexistence in finite samples has lacked a unified microscopic explanation.\r\n\r\nHere we show that this missing link is provided by the quantization of edge states by physically consistent boundary conditions. Starting from the Landau problem in finite geometries, we show that Dirichlet, Neumann, and mixed (Robin) boundary conditions discretize the guiding-center coordinate and the longitudinal momentum of edge states, generating families of chiral edge channels with boundary-dependent multiplicities. When incorporated into the Landauer–Büttiker transport formalism, these multiplicities naturally produce the integer Hall plateaus and a structured hierarchy of fractional filling factors.\r\n\r\nWe further show that retaining a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum without modifying the bulk Landau levels, enabling the strong-field fractional plateaus observed experimentally. Boundary quantization, refined by weak parity breaking, produces a fine structure of edge energies in which selected chiral branches remain pinned to the Fermi level, providing a unified microscopic foundation for quantized Hall transport across both integer and fractional regimes.","manuscriptTitle":"Unified microscopic theory of integer and fractional quantum Hall effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 12:49:39","doi":"10.21203/rs.3.rs-8689913/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6d68c90f-5336-40c8-ae07-cafd8d115189","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61740830,"name":"Physical sciences/Physics/Condensed-matter physics/Quantum Hall"},{"id":61740831,"name":"Physical sciences/Physics/Quantum physics/Quantum mechanics"}],"tags":[],"updatedAt":"2026-01-30T08:51:11+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 12:49:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8689913","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8689913","identity":"rs-8689913","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}