Half-Quantized Layer Hall Effect as a Probe of Quantized Axion Field

Half-Quantized Layer Hall Effect as a Probe of Quantized Axion Field | 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 Half-Quantized Layer Hall Effect as a Probe of Quantized Axion Field Di Xiao, Jiayuan Hu, Binbin Wang, Humian Zhou, Tongtong Jia, Zheng Sun, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7021873/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Jan, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract The layer Hall effect (LHE), an emergent Berry-curvature phenomenon encoded in the spatial degrees of freedom, establishes new transport paradigms in topological quantum matter 1,2 . The axion insulator hosts a quantized axion field, which manifests through two intertwined phenomena 3–7 : (i) a bulk topological magnetoelectric (TME) effect, and (ii) a surface-layer Hall effect with half-quantized anomalous Hall conductance (AHC). Hence, the magnetic axion insulator heterostructures 8–10 provide an ideal condensed matter platform to investigate the quantization of such layer Hall effects; however, its unambiguous experimental detection remains a significant challenge. Here, we employ precision molecular beam epitaxy (MBE) of (Bi,Sb) 2 Te 3 topological insulator (TI) sandwich structures to construct prototypical axion insulators with atomically controlled magnetic interfaces. Through electrical gating, we demonstrate selective surface state manipulation via asymmetric Fermi level positioning. Crucially, by maintaining one surface within the magnetic gap while displacing the other into metallic conduction regimes, both parallel and antiparallel magnetization configurations exhibit half-quantized AHC s xy = 0.5 e ² /h in over 10 devices (where e is the elementary charge, and h is the Planck’s constant). The observed layer-resolved half-quantization establishes two fundamental advances: (i) experimental realization of the half-quantized layer Hall effect, and (ii) direct electrical manifestation of a quantized axion field. Our findings not only resolve longstanding debates regarding experimental verification of the quantized axion field in magnetic TIs, but also establish a metrological framework for spatially resolved engineering of the quantized topological response. Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological insulators Physical sciences/Physics/Condensed-matter physics/Quantum Hall Physical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films Physical sciences/Physics/Electronics, photonics and device physics/Electronic and spintronic devices Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation0701.docx Supplementary Information Cite Share Download PDF Status: Published Journal Publication published 07 Jan, 2026 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. 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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-7021873","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":479587073,"identity":"f018de86-c523-4134-a155-e79e54eb0e52","order_by":0,"name":"Di Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYDACZiDmMZCQ45dgbGBIKJAgWouFseQMkBYDYrSAAA9DReKGGyCWARGqDY4zP3zwpkCCcfPt5uYPDwws5PmlGxg/fMzBrUWymc3YcI6BBLPZnYNtEkCHGc6cc4BZcuY23Fr4mRnMpIHeZzO7kdgG8kuCwY0ENmZePFrYmNm/gbTwGM9IbP5AlBZ+Zh6wLRIGEokNEkRpkWzmKQb5xUAC6DCIX4DW4fWLwfnjGx+8+VNX3z8j/fHHHxV18vwSyQc/fMSjBRsAxukoGAWjYBSMAsoAAA2NRybiRsGFAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2894-034X","institution":"Huawei Technologies Co., LTD","correspondingAuthor":true,"prefix":"","firstName":"Di","middleName":"","lastName":"Xiao","suffix":""},{"id":479587074,"identity":"b78fbca8-eec8-4a79-ad29-5eac50168a34","order_by":1,"name":"Jiayuan Hu","email":"","orcid":"","institution":"Huawei Technologies Co., Ltd.","correspondingAuthor":false,"prefix":"","firstName":"Jiayuan","middleName":"","lastName":"Hu","suffix":""},{"id":479587075,"identity":"d98945e1-9541-43f0-8885-cedea61e50aa","order_by":2,"name":"Binbin Wang","email":"","orcid":"","institution":"Huawei Technologies Co., Ltd.","correspondingAuthor":false,"prefix":"","firstName":"Binbin","middleName":"","lastName":"Wang","suffix":""},{"id":479587076,"identity":"9a6186e4-dcb6-4753-a7df-d248aad23630","order_by":3,"name":"Humian Zhou","email":"","orcid":"","institution":"International Center for Quantum Materials, School of Physics, Peking University","correspondingAuthor":false,"prefix":"","firstName":"Humian","middleName":"","lastName":"Zhou","suffix":""},{"id":479587077,"identity":"19118a6f-ff4d-4427-b9e9-d294e56d5c76","order_by":4,"name":"Tongtong Jia","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Tongtong","middleName":"","lastName":"Jia","suffix":""},{"id":479587078,"identity":"ebc4d28c-e79d-46e8-bbeb-cbdb9e7179c6","order_by":5,"name":"Zheng Sun","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Zheng","middleName":"","lastName":"Sun","suffix":""},{"id":479587079,"identity":"a26baf4e-5034-4e0a-8866-ddb1f0901ec1","order_by":6,"name":"Chang Liu","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Chang","middleName":"","lastName":"Liu","suffix":""},{"id":479587080,"identity":"295a6227-5aa7-4e65-b080-f45cd8791df1","order_by":7,"name":"Bo Zhang","email":"","orcid":"","institution":"Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Zhang","suffix":""},{"id":479587081,"identity":"cf931c31-e281-4a86-a773-07dd37ae3b4c","order_by":8,"name":"Dong Qian","email":"","orcid":"https://orcid.org/0000-0001-5891-8138","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Dong","middleName":"","lastName":"Qian","suffix":""},{"id":479587082,"identity":"20d60794-a4a6-4bb2-8b27-4409b3f0eb25","order_by":9,"name":"Tingxin Li","email":"","orcid":"https://orcid.org/0000-0002-3572-4530","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Tingxin","middleName":"","lastName":"Li","suffix":""},{"id":479587083,"identity":"4357a948-4988-4951-8c06-4cef356f97e2","order_by":10,"name":"X. 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The axion insulator hosts a quantized axion field, which manifests through two intertwined phenomena\u003csup\u003e3–7\u003c/sup\u003e: (i) a bulk topological magnetoelectric (TME) effect, and (ii) a surface-layer Hall effect with half-quantized anomalous Hall conductance (AHC). Hence, the magnetic axion insulator heterostructures\u003csup\u003e8–10\u003c/sup\u003e provide an ideal condensed matter platform to investigate the quantization of such layer Hall effects; however, its unambiguous experimental detection remains a significant challenge. Here, we employ precision molecular beam epitaxy (MBE) of (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e topological insulator (TI) sandwich structures to construct prototypical axion insulators with atomically controlled magnetic interfaces. Through electrical gating, we demonstrate selective surface state manipulation via asymmetric Fermi level positioning. Crucially, by maintaining one surface within the magnetic gap while displacing the other into metallic conduction regimes, both parallel and antiparallel magnetization configurations exhibit half-quantized AHC \u003cem\u003es\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e = 0.5 \u003cem\u003ee\u003c/em\u003e²\u003cem\u003e/h\u003c/em\u003e in over 10 devices (where \u003cem\u003ee\u003c/em\u003e is the elementary charge, and \u003cem\u003eh\u003c/em\u003e is the Planck’s constant). The observed layer-resolved half-quantization establishes two fundamental advances: (i) experimental realization of the half-quantized layer Hall effect, and (ii) direct electrical manifestation of a quantized axion field. Our findings not only resolve longstanding debates regarding experimental verification of the quantized axion field in magnetic TIs, but also establish a metrological framework for spatially resolved engineering of the quantized topological response.\u003c/p\u003e","manuscriptTitle":"Half-Quantized Layer Hall Effect as a Probe of Quantized Axion Field","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-03 06:52:54","doi":"10.21203/rs.3.rs-7021873/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":"e1159193-acd5-4eff-b7d9-1963f279ca87","owner":[],"postedDate":"July 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":50925929,"name":"Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological insulators"},{"id":50925930,"name":"Physical sciences/Physics/Condensed-matter physics/Quantum Hall"},{"id":50925931,"name":"Physical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films"},{"id":50925932,"name":"Physical sciences/Physics/Electronics, photonics and device physics/Electronic and spintronic devices"},{"id":50925933,"name":"Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2026-02-04T08:18:09+00:00","versionOfRecord":{"articleIdentity":"rs-7021873","link":"https://doi.org/10.1038/s41467-025-68071-y","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2026-01-07 05:00:00","publishedOnDateReadable":"January 7th, 2026"},"versionCreatedAt":"2025-07-03 06:52:54","video":"","vorDoi":"10.1038/s41467-025-68071-y","vorDoiUrl":"https://doi.org/10.1038/s41467-025-68071-y","workflowStages":[]},"version":"v1","identity":"rs-7021873","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7021873","identity":"rs-7021873","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}