Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor

Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor | 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 Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor Masaru Kato, Terukazu Nishizaki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8751691/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 10 You are reading this latest preprint version Abstract Superconductor in nano-sized shape is investigated. Superconductor and also electrons which form superconductivity have quantum nature. This means when size of superconductor is small, there appear quantum effects.The critical temperature becomes higher than that of a bulk superconductor.In the extremely dirty nano-sized superconductor, the critical temperature becomes much higherthan that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has ahigh density of states.We show how this localized state of superconducting electrons developswith decreasing temperature just below the critical temperature. Critical temperature Dirty superconductor Nano-sized superconductor Bogoliubov-de Gennes equations Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 19 Mar, 2026 Reviews received at journal 19 Mar, 2026 Reviews received at journal 18 Mar, 2026 Reviewers agreed at journal 03 Mar, 2026 Reviewers agreed at journal 02 Mar, 2026 Reviewers agreed at journal 27 Feb, 2026 Reviewers invited by journal 10 Feb, 2026 Editor assigned by journal 04 Feb, 2026 Submission checks completed at journal 02 Feb, 2026 First submitted to journal 31 Jan, 2026 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-8751691","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591607895,"identity":"4bc7dc61-7481-4584-9f45-bcceaed055b3","order_by":0,"name":"Masaru Kato","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYDACHiBm/GcjB+MzE6OFsYGBLc2YZC2HEhuIdpduz+HnDz7wHEjvFztjwPCjhoHdnJAWs7Ntho0zJO7kzpydY8DYc4yB2ZKQfWbnGQybeQye5W64nWPAwNvAwGxwgKAW9o/NPAmH0w2AWhj/EqXlbA/QlgOHE0BamImz5cyZwpkzG9IMZ85OKzgsc0yCCL+cSd/w4WODjTy/dPLGh29qbJIJhhgKADpJItmAJC0gYEe6llEwCkbBKBjuAAAKAkApfhD8ewAAAABJRU5ErkJggg==","orcid":"","institution":"Osaka Metropolitan University","correspondingAuthor":true,"prefix":"","firstName":"Masaru","middleName":"","lastName":"Kato","suffix":""},{"id":591607897,"identity":"1d1e8e13-d012-4ed3-a312-71a879939cca","order_by":1,"name":"Terukazu Nishizaki","email":"","orcid":"","institution":"Kyushu Sangyo University","correspondingAuthor":false,"prefix":"","firstName":"Terukazu","middleName":"","lastName":"Nishizaki","suffix":""}],"badges":[],"createdAt":"2026-01-31 17:38:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8751691/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8751691/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102749263,"identity":"67c7a884-0ab5-4c97-bac5-ca311d56e25a","added_by":"auto","created_at":"2026-02-16 09:12:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5778110,"visible":true,"origin":"","legend":"","description":"","filename":"MKATOLT30.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8751691/v1_covered_b3a7d051-0638-40be-a49f-cc6e7918961a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-low-temperature-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jltp","sideBox":"Learn more about [Journal of Low Temperature Physics](http://link.springer.com/journal/10909)","snPcode":"10909","submissionUrl":"https://submission.nature.com/new-submission/10909/3","title":"Journal of Low Temperature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Critical temperature, Dirty superconductor, Nano-sized superconductor, Bogoliubov-de Gennes equations","lastPublishedDoi":"10.21203/rs.3.rs-8751691/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8751691/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Superconductor in nano-sized shape is investigated. Superconductor and also electrons which form superconductivity have quantum nature. This means when size of superconductor is small, there appear quantum effects.The critical temperature becomes higher than that of a bulk superconductor.In the extremely dirty nano-sized superconductor, the critical temperature becomes much higherthan that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has ahigh density of states.We show how this localized state of superconducting electrons developswith decreasing temperature just below the critical temperature. ","manuscriptTitle":"Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-16 05:04:15","doi":"10.21203/rs.3.rs-8751691/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-19T17:04:48+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-19T17:00:20+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-18T04:45:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"252750703300323733962895547446632814291","date":"2026-03-03T14:00:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"50418941511130760396762909507752008249","date":"2026-03-02T22:22:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"172766019518072731197830077159213046671","date":"2026-02-28T02:46:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-10T17:47:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-04T19:14:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-02T12:59:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Low Temperature Physics","date":"2026-01-31T17:29:36+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-low-temperature-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jltp","sideBox":"Learn more about [Journal of Low Temperature Physics](http://link.springer.com/journal/10909)","snPcode":"10909","submissionUrl":"https://submission.nature.com/new-submission/10909/3","title":"Journal of Low Temperature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"60405676-04c5-409a-b8ab-8c50e3426a3f","owner":[],"postedDate":"February 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-11T14:12:37+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-16 05:04:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8751691","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8751691","identity":"rs-8751691","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}