Planck quantization pseudogap in high-temperature superconductors

Planck quantization pseudogap in high-temperature superconductors | 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Article Planck quantization pseudogap in high-temperature superconductors Xiuqing Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6493159/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 behavior of the pseudogap phase is a major enigma in the superconductivity mechanism. It can either aid or hinder superconductivity, and the origins of the two gaps in high-temperature superconductors are still unknown. Based on Planck's quantum theory and polyhedral quantum well confinement in real space, we theoretically derived an inverse-square superconducting equation like Newton's and Coulomb's laws. This equation accurately predicts the superconducting transition temperatures of almost all copper- and iron-based superconducting materials, with theoretical and experimental results in agreement. This paper details the relationships among the superconducting nematic phase, the pseudogap phase, and doping concentration. We argue that the superconducting state corresponds to Planck's ground state, while the pseudogap state is Planck's excited state. Theoretical results show the pseudogap has no linear relation with doping concentration. Instead, as doping concentration drops, the pseudogap changes stepwise like the quantum Hall effect, with step depth determined by the Planck energy level. We also clarify the relationship among the specific heat jump near the superconducting transition temperature, doping concentration, and Planck energy level. These findings offer profound insights into the correlation between the pseudogap phase and superconductivity in cuprate superconductors. Given that both the superconducting and pseudogap stem from Planck's energy quantization, it is inferred that all superconductors may share the same superconducting mechanism. Theoretical Physics pseudogap phase Planck's ground state specific heat high-temperature superconductors 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-6493159","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":445585183,"identity":"8065319f-9b57-431d-b3a4-450aee771542","order_by":0,"name":"Xiuqing Huang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIiWNgGAWjYDACZiBOAGIDMK9CQk6eRC1nLIwNG4i1DayFsa0ikeEAIZXHeQxvPNxRy2Aukfzs4dd5EgmMDcwPH93Ao0WymcfYIvHMcQbLGWnmxrLbJPLYGdiMjXPwaOFn5jGTSGw7xmBwI8FMWnKbRDFjAw+bND4tbAgt6d+kJedIJDYcIKAFaksNUEuOmeTHBiK0SDazFVskth1gMDjzpkya4ZiEsWEzAb8YnD+88ebPtjpg0KVvk/xRUycnz9788DE+LSAgwcBwuL4ByGDmAXGZCSiHaqkDMxh/EKF6FIyCUTAKRh4AAOWoRefAa5X+AAAAAElFTkSuQmCC","orcid":"","institution":"National Laboratory of Solid State Microstructures of Physics, Nanjing University, Nanjing 210093, China","correspondingAuthor":true,"prefix":"","firstName":"Xiuqing","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2025-04-21 06:46:27","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-6493159/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6493159/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81096323,"identity":"2ca1a4d8-2c59-47d8-b7ce-92b38bbaa06a","added_by":"auto","created_at":"2025-04-22 08:02:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2397621,"visible":true,"origin":"","legend":"","description":"","filename":"plank.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6493159/v1_covered_2c15d318-ca1a-42e3-8ead-afb7caf89744.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePlanck quantization pseudogap in high-temperature superconductors\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"National Laboratory of Solid State Microstructures of Physics, Nanjing University, Nanjing 210093, China","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":"pseudogap phase, Planck's ground state, specific heat, high-temperature superconductors","lastPublishedDoi":"10.21203/rs.3.rs-6493159/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6493159/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe behavior of the pseudogap phase is a major enigma in the superconductivity mechanism. 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Instead, as doping concentration drops, the pseudogap changes stepwise like the quantum Hall effect, with step depth determined by the Planck energy level. We also clarify the relationship among the specific heat jump near the superconducting transition temperature, doping concentration, and Planck energy level. These findings offer profound insights into the correlation between the pseudogap phase and superconductivity in cuprate superconductors. 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