Impact of gap anisotropy of Polar and Anderson-Brinkman-Morel p-wave superconductors on thermoelectric properties of quantum dot hybrids

Impact of gap anisotropy of Polar and Anderson-Brinkman-Morel p-wave superconductors on thermoelectric properties of quantum dot hybrids | 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 Article Impact of gap anisotropy of Polar and Anderson-Brinkman-Morel p-wave superconductors on thermoelectric properties of quantum dot hybrids Vrishali Sonar, Piotr Trocha This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8353627/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract We theoretically investigate the thermoelectric transport properties of a hybrid device consisting of a quantum dot (QD) coupled to a ferromagnetic lead and a p-wave, spin-triplet superconducting electrode. We focus on two distinct phases - the Polar and Anderson-Brinkman-Morel (ABM) - both having anisotropic gap structure and pure spin-triplet pairing. To capture the momentum dependent tunneling between the QD and the triplet superconductor (TSC), we introduce a phenomenological angle dependent weighting of the QD-TSC coupling, and analyze two configurations in which superconducting symmetry axis is parallel or perpendicular to the tunneling axis. Employing the Keldysh Green’s function formalism in linear response regime, we compute key transport coefficients - electrical and thermal conductances, thermopower, and the thermoelectric figure of merit, based on anisotropy strength parameter.The results reveal that anisotropy plays crucial role in transport properties, and neglecting it in modeling conceals important qualitative signatures. Transport coefficients exhibit phase, geometry and anisotropy strength sensitive behaviors, thereby making them potential probes of superconducting order parameter and nodal orientation. Our formulation allows to separately quantify contribution of Andreev reflection and quasiparticle tunneling, and shows that, by mere rotation of crystallographic axis of the superconductor, it is possible to obstruct or maximize the effective (triplet) Andreev reflection. In the ABM state, the origin of orientation-dependent suppression of Andreev reflection is traced to the azimuthal phase dependence. Moreover, the thermal conductance is enhanced by few orders of magnitude compared to conventional s-wave case. The results demonstrate that the anisotropic, orientation-dependent triplet gap strongly governs transport, offering experimentally accessible signatures of the superconducting phase and nodal structure. Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryinformationSonarTrocha.pdf Cite Share Download PDF Status: Published Journal Publication published 16 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 19 Feb, 2026 Reviews received at journal 17 Feb, 2026 Reviews received at journal 10 Feb, 2026 Reviewers agreed at journal 31 Jan, 2026 Reviewers agreed at journal 30 Jan, 2026 Reviewers agreed at journal 30 Jan, 2026 Reviewers agreed at journal 29 Jan, 2026 Reviews received at journal 18 Jan, 2026 Reviewers agreed at journal 28 Dec, 2025 Reviewers invited by journal 28 Dec, 2025 Editor invited by journal 23 Dec, 2025 Editor assigned by journal 18 Dec, 2025 Submission checks completed at journal 18 Dec, 2025 First submitted to journal 13 Dec, 2025 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-8353627","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":576249416,"identity":"be47a888-095c-402b-8325-4f28233be727","order_by":0,"name":"Vrishali Sonar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIie3PMQrCMBSA4YSuBdcWhFwhIAhOHsQl4uDSgOBSQSUgtEvdC4peQRfnlEJdoq6KInoDwaVuJo5Cbd0E8w/hDe8jCQA63Q9nAgtATlw5GgYrTAAnQhFYjIAXgZ6acgjyx9G9553LaDK68Ots0Cj5kqTuKpNgsW3ZG69r4lOCeXO1pmEMGQzEMZtYDraZICa2iCIJZZIY0MsmKHQqD0VQ2L7x5jSh8zwC9k7VZi4x5SBvYX26yCNYiGpNEbx3OpwknC4liT79BflB5cAwqcuHLa9pf0hnuzi6pO6Hh70Vv05eeF82/GZZp9Pp/qQnAuVfzQSNU8YAAAAASUVORK5CYII=","orcid":"","institution":"Adam Mickiewicz University in Poznań","correspondingAuthor":true,"prefix":"","firstName":"Vrishali","middleName":"","lastName":"Sonar","suffix":""},{"id":576249417,"identity":"26d526d4-b04d-4641-a0a1-dc39861fb041","order_by":1,"name":"Piotr Trocha","email":"","orcid":"","institution":"Adam Mickiewicz University in Poznań","correspondingAuthor":false,"prefix":"","firstName":"Piotr","middleName":"","lastName":"Trocha","suffix":""}],"badges":[],"createdAt":"2025-12-13 15:08:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8353627/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8353627/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-46160-2","type":"published","date":"2026-04-16T15:58:45+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100587466,"identity":"a9e839fe-e39b-4a29-91f7-c01c317815fe","added_by":"auto","created_at":"2026-01-19 12:14:43","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4972,"visible":true,"origin":"","legend":"","description":"","filename":"93d07ed7370b4bae978a1d5a4d76f181.json","url":"https://assets-eu.researchsquare.com/files/rs-8353627/v1/9becd773a4941a8718381f16.json"},{"id":107350844,"identity":"f698c9d3-801b-44f2-b097-ff1a1c20a116","added_by":"auto","created_at":"2026-04-20 16:05:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":803416,"visible":true,"origin":"","legend":"","description":"","filename":"ScientificReportsSonarTrocharevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8353627/v1_covered_7d3bad90-98a9-45f0-96e5-443a63b5eb17.pdf"},{"id":100587499,"identity":"a2b315fd-e538-4dbe-83a7-7a1de2a96637","added_by":"auto","created_at":"2026-01-19 12:15:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":484647,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryinformationSonarTrocha.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8353627/v1/754778703802764fc062546a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Impact of gap anisotropy of Polar and Anderson-Brinkman-Morel p-wave superconductors on thermoelectric properties of quantum dot hybrids","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":true,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8353627/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8353627/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We theoretically investigate the thermoelectric transport properties of a hybrid device consisting of a quantum dot (QD) coupled to a ferromagnetic lead and a p-wave, spin-triplet superconducting electrode. We focus on two distinct phases - the Polar and Anderson-Brinkman-Morel (ABM) - both having anisotropic gap structure and pure spin-triplet pairing. To capture the momentum dependent tunneling between the QD and the triplet superconductor (TSC), we introduce a phenomenological angle dependent weighting of the QD-TSC coupling, and analyze two configurations in which superconducting symmetry axis is parallel or perpendicular to the tunneling axis. Employing the Keldysh Green’s function formalism in linear response regime, we compute key transport coefficients - electrical and thermal conductances, thermopower, and the thermoelectric figure of merit, based on anisotropy strength parameter.The results reveal that anisotropy plays crucial role in transport properties, and neglecting it in modeling conceals important qualitative signatures. Transport coefficients exhibit phase, geometry and anisotropy strength sensitive behaviors, thereby making them potential probes of superconducting order parameter and nodal orientation. Our formulation allows to separately quantify contribution of Andreev reflection and quasiparticle tunneling, and shows that, by mere rotation of crystallographic axis of the superconductor, it is possible to obstruct or maximize the effective (triplet) Andreev reflection. In the ABM state, the origin of orientation-dependent suppression of Andreev reflection is traced to the azimuthal phase dependence. Moreover, the thermal conductance is enhanced by few orders of magnitude compared to conventional s-wave case. The results demonstrate that the anisotropic, orientation-dependent triplet gap strongly governs transport, offering experimentally accessible signatures of the superconducting phase and nodal structure.","manuscriptTitle":"Impact of gap anisotropy of Polar and Anderson-Brinkman-Morel p-wave superconductors on thermoelectric properties of quantum dot hybrids","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-19 12:06:37","doi":"10.21203/rs.3.rs-8353627/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-19T12:52:06+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-18T03:34:16+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-11T04:39:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326308348846450865984412562050872767396","date":"2026-01-31T13:17:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"225902767909113354608406895613323292548","date":"2026-01-31T00:09:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"29656766530480794169639295914383790341","date":"2026-01-30T12:57:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"336575828097472245307656508644160718679","date":"2026-01-30T01:55:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-18T09:12:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"133482530180082746466572208000038806043","date":"2025-12-29T02:48:57+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-28T13:02:40+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-23T13:05:58+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-18T08:44:07+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-18T08:41:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-13T14:58:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"84021831-d580-4184-b37a-7555759f4141","owner":[],"postedDate":"January 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":61313204,"name":"Physical sciences/Materials science"},{"id":61313205,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-04-20T16:02:55+00:00","versionOfRecord":{"articleIdentity":"rs-8353627","link":"https://doi.org/10.1038/s41598-026-46160-2","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-04-16 15:58:45","publishedOnDateReadable":"April 16th, 2026"},"versionCreatedAt":"2026-01-19 12:06:37","video":"","vorDoi":"10.1038/s41598-026-46160-2","vorDoiUrl":"https://doi.org/10.1038/s41598-026-46160-2","workflowStages":[]},"version":"v1","identity":"rs-8353627","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8353627","identity":"rs-8353627","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}