Minimal geometric correction to vortex interactions in GL

Minimal geometric correction to vortex interactions in GL | 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Article Minimal geometric correction to vortex interactions in GL Miguel Jorge Diaz Luna This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8702861/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 introduce a minimal, gauge-invariant geometric correction within the Ginzburg–Landau (GL) framework that modifies intervortex interactions without introducing additional dynamical fields. The correction is encoded as a weak, smooth modulation of an effective GL length scale, providing a compact parameterization of geometry-induced mesoscopic effects beyond the homogeneous GL limit. In the London regime, we derive the leading-order correction to the intervortex potential and obtain an analytic criterion that delineates a crossover between bulk-like and mesoscopic interaction regimes. Two simple model profiles are discussed, illustrating how the approach reproduces qualitative macroscopic–mesoscopic transitions reported in time-dependent GL simulations. The microscopic origin of the effective modulation is intentionally left open, establishing a controlled and GL-consistent entry point for future theoretical and numerical investigations. Hard Condensed-matter Physics vortex interactions Ginzburg–Landau theory London limit mesoscopic superconductivity geometric modulation type-II superconductors intervortex potential 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-8702861","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580685357,"identity":"7dfcf323-8c54-43ab-8d96-ed64ee51ce35","order_by":0,"name":"Miguel Jorge Diaz Luna","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYFCCA4YHEir+1/OD2AkFxGkxOPDgDHOCZANIiwFx1hgcfNjGnGBwAMwmQr1u4+ENBxLb2PKMz69O/PDAgEGeX+wAfi1mB44VHEg4x1NsduPtZgmgwwxnzk4gpOWMwYGEMgnGbTfObgBpSTC4TZQWNgPGzTPObv5Bgpa2hMQN/L3biLUF5JczB4wlbvBus0gwkCDCLzcOb3z4o+KAHH//2c03f1TYyPNLE9DCIHEAxgCrlCCgHAT4G2CMA3hUjYJRMApGwYgGALOHUyYrLK0zAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0002-2921-8903","institution":"Independent researcher","correspondingAuthor":true,"prefix":"","firstName":"Miguel","middleName":"Jorge Diaz","lastName":"Luna","suffix":""}],"badges":[],"createdAt":"2026-01-26 17:41:55","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-8702861/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8702861/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101297417,"identity":"fa9c624a-80dc-4a10-91e5-5472a8f73cbe","added_by":"auto","created_at":"2026-01-28 09:27:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":504561,"visible":true,"origin":"","legend":"","description":"","filename":"MinimalgeometriccorrectiontovortexinteractionsinGL.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8702861/v1_covered_86613a09-9124-470b-9fbb-4e154379108d.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMinimal geometric correction to vortex interactions in GL\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","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":"vortex interactions, Ginzburg–Landau theory, London limit, mesoscopic superconductivity, geometric modulation, type-II superconductors, intervortex potential","lastPublishedDoi":"10.21203/rs.3.rs-8702861/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8702861/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce a minimal, gauge-invariant geometric correction within the Ginzburg–Landau (GL) framework that modifies intervortex interactions without introducing additional dynamical fields. The correction is encoded as a weak, smooth modulation of an effective GL length scale, providing a compact parameterization of geometry-induced mesoscopic effects beyond the homogeneous GL limit. In the London regime, we derive the leading-order correction to the intervortex potential and obtain an analytic criterion that delineates a crossover between bulk-like and mesoscopic interaction regimes. Two simple model profiles are discussed, illustrating how the approach reproduces qualitative macroscopic–mesoscopic transitions reported in time-dependent GL simulations. The microscopic origin of the effective modulation is intentionally left open, establishing a controlled and GL-consistent entry point for future theoretical and numerical investigations.\u003c/p\u003e","manuscriptTitle":"Minimal geometric correction to vortex interactions in GL","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-28 04:14:09","doi":"10.21203/rs.3.rs-8702861/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":"cbc2aa79-b41c-4d88-be2d-cc916eb4cb9e","owner":[],"postedDate":"January 28th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61774521,"name":"Hard Condensed-matter Physics"}],"tags":[],"updatedAt":"2026-01-28T04:14:09+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-28 04:14:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8702861","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8702861","identity":"rs-8702861","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}