The Role of Quasiperiodicity on the Electronic Structure of Elements

The Role of Quasiperiodicity on the Electronic Structure of Elements | 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 The Role of Quasiperiodicity on the Electronic Structure of Elements Satish Prajapati This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9203395/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 The discovery of quasicrystals established that long-range atomic order does not require translational periodicity. Yet whether quasiperiodic order alone determines electronic structure—specifically the pseudogap at the Fermi level—remains unresolved. Here we present a definitive computational test using alkali metal (Na, K) monolayers on icosahedral Al-Pd-Mn, a system where quasiperiodic order is isolated from chemical complexity. Contrary to the prevailing hypothesis, we find no pseudogap in these perfectly ordered quasiperiodic monolayers. The density of states is indistinguishable from free-electron behavior with 𝑁(𝐸𝐹) = 0.32 ± 0.03 (Na) and 0.28 ± 0.03 (K) states/eV/atom. The quasiperiodic potential strength is an order of magnitude too weak (∣ 𝑉(𝐆∥) ∣≈ 0.05 eV), and the Hume-Rothery condition 2𝑘𝐹 =∣ 𝐆∥ ∣ fails by 8% (Na) and 12% (K). Orbital decomposition reveals negligible 𝑠 -𝑑 hybridization with charge transfer <0.05𝑒 per atom. These results establish that quasiperiodicity alone is insufficient to induce a pseudogap; strong orbital hybridization and precise Fermi surface resonance are required. We present a unified phase diagram that collapses all calculated data onto a single scaling function, enabling quantitative predictions for strain engineering (8% tensile on Na) and alloying (7% Pb in Na). This work resolves a fundamental question in quasicrystal physics and provides design principles for aperiodic materials. Materials Engineering Materials Chemistry Materials Theory and Modeling Electronic Materials and Devices Magnetics Materials and Devices Density of states (DOS) Fermi level Electronic structure Pseudogap Quasicrystals Quasiperiodic monolayers Approximants Density functional theory (DFT) Kernel polynomial method (KPM) Pair distribution function Fermi surface Fourier components Hume-Rothery mechanism s-d hybridization Alloy engineering Orbital engineering Quantum transport Berry curvature Alkali metal monolayers electronic structure Full Text Additional Declarations The authors declare no competing interests. Supplementary Files Supplementarypaper.pdf Supplementary Information 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-9203395","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":610878938,"identity":"9e250789-5179-408b-be15-f1c41407d73a","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":"2026-03-23 17:31:24","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-9203395/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9203395/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105564811,"identity":"5e0eef87-ac45-43c7-b5fb-a9d5e4e18643","added_by":"auto","created_at":"2026-03-27 12:50:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3489001,"visible":true,"origin":"","legend":"","description":"","filename":"TheRoleofQuasiperiodicityontheElectronicStructureofElements.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9203395/v1_covered_041c1acb-f3ea-4921-92c4-3464adc73fb9.pdf"},{"id":105373291,"identity":"575b2969-d023-44e3-96a1-50f2ee2a982b","added_by":"auto","created_at":"2026-03-25 09:50:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2265691,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupplementary Information\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Supplementarypaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9203395/v1/d5e1d6ccb9b7de5870c863e6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eThe Role of Quasiperiodicity on the Electronic Structure of Elements\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Government College of Engineering And Ceramic Technology","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":"Density of states (DOS), Fermi level, Electronic structure, Pseudogap, Quasicrystals, Quasiperiodic monolayers, Approximants, Density functional theory (DFT), Kernel polynomial method (KPM), Pair distribution function, Fermi surface, Fourier components, Hume-Rothery mechanism, s-d hybridization, Alloy engineering, Orbital engineering, Quantum transport, Berry curvature, Alkali metal monolayers, electronic structure","lastPublishedDoi":"10.21203/rs.3.rs-9203395/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9203395/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eThe discovery of quasicrystals established that long-range atomic order does not require \u0026nbsp;translational periodicity. Yet whether quasiperiodic order alone determines electronic \u0026nbsp;structure—specifically the pseudogap at the Fermi level—remains unresolved. Here we present \u0026nbsp;a definitive computational test using alkali metal (Na, K) monolayers on icosahedral Al-Pd-Mn, a \u0026nbsp;system where quasiperiodic order is isolated from chemical complexity. Contrary to the prevailing \u0026nbsp;hypothesis, we find no pseudogap in these perfectly ordered quasiperiodic monolayers. The \u0026nbsp;density of states is indistinguishable from free-electron behavior with 𝑁(𝐸𝐹) = 0.32 ± 0.03 (Na) \u0026nbsp;and 0.28 ± 0.03 (K) states/eV/atom. The quasiperiodic potential strength is an order of \u0026nbsp;magnitude too weak (∣ 𝑉(𝐆∥) ∣≈ 0.05 eV), and the Hume-Rothery condition 2𝑘𝐹 =∣ 𝐆∥ ∣ fails by \u0026nbsp;8% (Na) and 12% (K). Orbital decomposition reveals negligible 𝑠 -𝑑 hybridization with charge \u0026nbsp;transfer \u0026lt;0.05𝑒 per atom. These results establish that quasiperiodicity alone is insufficient to \u0026nbsp;induce a pseudogap; strong orbital hybridization and precise Fermi surface resonance are \u0026nbsp;required. We present a unified phase diagram that collapses all calculated data onto a single \u0026nbsp;scaling function, enabling quantitative predictions for strain engineering (8% tensile on Na) and \u0026nbsp;alloying (7% Pb in Na). This work resolves a fundamental question in quasicrystal physics and \u0026nbsp;provides design principles for aperiodic materials.\u003c/strong\u003e\u003c/p\u003e","manuscriptTitle":"The Role of Quasiperiodicity on the Electronic Structure of Elements","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-25 09:50:20","doi":"10.21203/rs.3.rs-9203395/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":"March 25th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65001031,"name":"Materials Engineering"},{"id":65001032,"name":"Materials Chemistry"},{"id":65001033,"name":"Materials Theory and Modeling"},{"id":65001034,"name":"Electronic Materials and Devices"},{"id":65001035,"name":"Magnetics Materials and Devices"}],"tags":[],"updatedAt":"2026-03-25T09:50:20+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-25 09:50:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9203395","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9203395","identity":"rs-9203395","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}