Interplay of Long-Range Hopping and Spatially Correlated Bond Disorder in the Topological Robustness of the Extended SSH Model

Interplay of Long-Range Hopping and Spatially Correlated Bond Disorder in the Topological Robustness of the Extended SSH Model | 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 Interplay of Long-Range Hopping and Spatially Correlated Bond Disorder in the Topological Robustness of the Extended SSH Model Matías Alfredo Gacitúa Ruiz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8240181/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 investigate the robustness of topological edge states in the Su-Schrieffer-Heeger (SSH) model extended with next-nearest-neighbor (NNN) hopping, under the influence of spatially correlated bond disorder. While uncorrelated (white) disorder is known to degrade topological invariants rapidly, we demonstrate that correlated disorder induces a resonant protection mechanism when the correlation length matches the hopping scales. By analyzing the real-space winding number and the inverse participation ratio (IPR) across finite-size scaling, we map out a phase diagram revealing regimes where topology survives beyond the standard Anderson localization limit. Our results suggest that engineering correlation in disorder can be a viable strategy to stabilize topological phases in noisy experimental platforms such as photonic lattices. Hard Condensed-matter Physics Topological Insulators SSH Model Correlated Disorder Anderson Localization Topological Robustness Edge States Full Text Additional Declarations The authors declare no competing interests. Supplementary Files plotpaper.py Source Code: Python Simulation Script for Reproducibility 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-8240181","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":552823940,"identity":"ba625df3-0a69-47a6-b462-23ec121db64f","order_by":0,"name":"Matías Alfredo Gacitúa Ruiz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYJCCAwwMEgwM7AyMD4AcHj7CGpihWpgZmA1AWtiI0QKj2SRANEEtuu3nDx6ubLOwZ2Bmflb5NcdOho2B+eGjG3i0mJ1JZjh4tk0C6Cw2s9uy25KBDmMzNs7Bp+UAUEtjmwTQbB6225LbgCTQO9J4tZx/DNbCA9JSLLmtnggtNyC2SIC0MH7cdpgYLY8NDjackzBgY2YzlmbcdpwHxMDvl/OJjz82lNXZ87M3P/z4c1s1mPEYnxY4AEUHMw+IxUxAJQpg/EGK6lEwCkbBKBgxAABoTTunvtyIrgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0000-9403-6423","institution":"Independent","correspondingAuthor":true,"prefix":"","firstName":"Matías","middleName":"Alfredo Gacitúa","lastName":"Ruiz","suffix":""}],"badges":[],"createdAt":"2025-11-30 05:25:07","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-8240181/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8240181/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97204691,"identity":"b408f11e-2a71-4ab1-bcbf-febdb1a930e9","added_by":"auto","created_at":"2025-12-02 02:28:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":260902,"visible":true,"origin":"","legend":"","description":"","filename":"InterplayofLongRangeHoppingandCorrelatedBondDisorderintheTopologicalRobustnessoftheSSHModel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8240181/v1_covered_f720ae96-a6d7-4211-b78d-1f7ba18bef88.pdf"},{"id":97204690,"identity":"0c8c87c1-4a1e-43d8-8801-90ada43e07ba","added_by":"auto","created_at":"2025-12-02 02:28:05","extension":"py","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":5465,"visible":true,"origin":"","legend":"\u003cp\u003eSource Code: Python Simulation Script for Reproducibility\u003c/p\u003e","description":"","filename":"plotpaper.py","url":"https://assets-eu.researchsquare.com/files/rs-8240181/v1/ec99595a0c9b385eb12a7d2c.py"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eInterplay of Long-Range Hopping and Spatially Correlated Bond Disorder in the Topological Robustness of the Extended SSH Model\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":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":"Topological Insulators, SSH Model, Correlated Disorder, Anderson Localization, Topological Robustness, Edge States","lastPublishedDoi":"10.21203/rs.3.rs-8240181/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8240181/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate the robustness of topological edge states in the Su-Schrieffer-Heeger (SSH) model extended with next-nearest-neighbor (NNN) hopping, under the influence of spatially correlated bond disorder. 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