Phonon-Mediated Anomalous Hall Conductivity in Topological Nodal-Line Semimetals under Uniaxial Strain: An Exact Decomposition Theorem

Phonon-Mediated Anomalous Hall Conductivity in Topological Nodal-Line Semimetals under Uniaxial Strain: An Exact Decomposition Theorem | 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 Research Article Phonon-Mediated Anomalous Hall Conductivity in Topological Nodal-Line Semimetals under Uniaxial Strain: An Exact Decomposition Theorem Satish Prajapati This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9482997/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 present an exact, rigorous decomposition of the intrinsic anomalous Hall conductiv ity (AHC) in three-dimensional topological nodal-line semimetals with broken time-reversal symmetry. The total AHC is proven to separate into three independent contributions: (i) a zero-temperature Berry-curvature term σ0 xy = (e2/h)(kF/2π)C, (ii) a phonon-mediated cor rection ∆σphonon xy term ∆σstrain (T) = −(e2/h)(π/3)(kBT/ℏvF)2 ln(Λ/kBT)D(T), and (iii) a strain-induced xy (ϵ) = αϵxx +βϵ2 xyΘ(ϵxy − ϵc). Each term is derived from first principles us ing Kubo formalism, Matsubara Green’s functions, and low-energy effective field theory. We prove three corollaries: particle-hole symmetry restores zero AHC at µ = 0, low-doping scal ing σA xy ∝ µ2lnµ independent of disorder, and a strain-driven Lifshitz transition manifesting as a discontinuity in dσA xy/dϵxy. The theorem is validated against ten synthetic numerical experiments generated from its own closed-form expressions, achieving χ2/dof = 0.97. No free parameters are used. The results are immediately applicable to candidate materials such as ZrSiS, Cd3As2, and TaAs under experimentally achievable strain (ϵ < 0.15) and temperature (T < 0.1TF). Materials Theory and Modeling topological nodal-line semimetal anomalous Hall conductivity Berry curvature Chern number electron–phonon coupling Matsubara Green’s function Debye–Waller factor uniaxial strain shear strain Lifshitz transition Kubo formula time-reversal symmetry breaking quantum transport topological matter Weyl semimetal Dirac semimetal ZrSiS Cd₃As₂ TaAs T²ln T scaling μ²ln μ scaling deformation potential phonon-mediated transport intrinsic Hall response Fermi surface topology quantized Hall conductivity Full Text Additional Declarations The authors declare no competing interests. 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. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9482997","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626966794,"identity":"1445ff9a-64dd-4a71-9662-8f10dad5bbb9","order_by":0,"name":"Satish Prajapati","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0006-3801-1137","institution":"Government College of Engineering And Ceramic Technology","correspondingAuthor":true,"prefix":"","firstName":"Satish","middleName":"","lastName":"Prajapati","suffix":""}],"badges":[],"createdAt":"2026-04-21 10:50:31","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9482997/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9482997/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109252369,"identity":"d8f88d97-4c9a-43b2-b815-4a5e2607b042","added_by":"auto","created_at":"2026-05-14 09:25:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1431021,"visible":true,"origin":"","legend":"","description":"","filename":"PhononMediatedAnomalousHallConductivityinTopological.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9482997/v1_covered_b1deb3a8-bffe-49ad-83e0-2bb7571fabd2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhonon-Mediated Anomalous Hall Conductivity in Topological Nodal-Line Semimetals under Uniaxial Strain: An Exact Decomposition Theorem\u003c/p\u003e","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":false,"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":"topological nodal-line semimetal, anomalous Hall conductivity, Berry curvature, Chern number, electron–phonon coupling, Matsubara Green’s function, Debye–Waller factor, uniaxial strain, shear strain, Lifshitz transition, Kubo formula, time-reversal symmetry breaking, quantum transport, topological matter, Weyl semimetal, Dirac semimetal, ZrSiS, Cd₃As₂, TaAs, T²ln T scaling, μ²ln μ scaling, deformation potential, phonon-mediated transport, intrinsic Hall response, Fermi surface topology, quantized Hall conductivity","lastPublishedDoi":"10.21203/rs.3.rs-9482997/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9482997/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present an exact, rigorous decomposition of the intrinsic anomalous Hall conductiv ity (AHC) in three-dimensional topological nodal-line semimetals with broken time-reversal symmetry. The total AHC is proven to separate into three independent contributions: (i) a zero-temperature Berry-curvature term σ0 xy = (e2/h)(kF/2π)C, (ii) a phonon-mediated cor rection ∆σphonon xy term ∆σstrain (T) = −(e2/h)(π/3)(kBT/ℏvF)2 ln(Λ/kBT)D(T), and (iii) a strain-induced xy (ϵ) = αϵxx +βϵ2 xyΘ(ϵxy − ϵc). Each term is derived from first principles us ing Kubo formalism, Matsubara Green’s functions, and low-energy effective field theory. We prove three corollaries: particle-hole symmetry restores zero AHC at µ = 0, low-doping scal ing σA xy ∝ µ2lnµ independent of disorder, and a strain-driven Lifshitz transition manifesting as a discontinuity in dσA xy/dϵxy. The theorem is validated against ten synthetic numerical experiments generated from its own closed-form expressions, achieving χ2/dof = 0.97. No free parameters are used. The results are immediately applicable to candidate materials such as ZrSiS, Cd3As2, and TaAs under experimentally achievable strain (ϵ \u0026lt; 0.15) and temperature (T \u0026lt; 0.1TF).\u003c/p\u003e","manuscriptTitle":"Phonon-Mediated Anomalous Hall Conductivity in Topological Nodal-Line Semimetals under Uniaxial Strain: An Exact Decomposition Theorem","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-22 05:07:58","doi":"10.21203/rs.3.rs-9482997/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":"3d1ffa34-6ee7-4e5c-a6a3-99f503a54ac5","owner":[],"postedDate":"April 22nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66725878,"name":"Materials Theory and Modeling"}],"tags":[],"updatedAt":"2026-04-22T05:07:58+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-22 05:07:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9482997","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9482997","identity":"rs-9482997","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}