Topology-enabled Quantum Toroidal Moment in Carbon Nanotori

Topology-enabled Quantum Toroidal Moment in Carbon Nanotori | 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 Topology-enabled Quantum Toroidal Moment in Carbon Nanotori Arkamita Bandyopadhyay, Jamal Berakdar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7930501/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Beside electric and magnetic dipoles, toroidal moments are another class of charge/current distributions with unique properties but are hard to realize, particularly on the quantum level. Here, optically active, toroidal electronic quantum stationary states are discovered in pristine, achiral carbon nano rings or tori such as C$ {120}$, C$ {144}$, and C$_{168}$ in a static electric field. Their utility as generators of nanoscale toroidal moment is illustrated. Although the molecules lack structural chirality, electric field-induced symmetry breaking enables coherent scattering from the topologically ordered ions resulting in toroidization of specific states in which electric and magnetic dipole moments intertwine such that both diminish but give rise to a finite toroidal moment, rending the molecule toroidal and magnetoelectric. The toroidal states are identified from the entirety of the ab-initio calculated spectrum by projecting onto toroidal harmonics and evaluating the electric, magnetic, and toroidal dipole moment which clarifies the microscopic origin of toroidization. Experimentally, the toroidal nature of these states entails optical activity which is confirmed by rotary power calculations. Importantly, the activated toroidal states are optically achievable with one photon transitions, leading to a toroidal dipole moment which is persistent and can be converted into a pulse of time-dependent toroidal dipole moment by switching off the static electric field. Furthermore, topological superatomic molecular orbitals (SAMOs) are discovered with charge distribution outside the fullerene tori and are found to exhibit pronounced toroidal or mixed toroidal–helical character. These new SAMOs provide natural way to generate nanoscale toroidal electromagnetic field and to induce optical activation of the enclosed valence states. Our findings provide a quantitative framework linking topology, orbital symmetry, toroidal response, and spectroscopic signatures in molecular tori. The results of the microscopic simulations and analysis are experimentally assessable by circular dichroism and have potential applications as further tools in optical control, field-driven manipulation, doping-induced chirality, and quantum information applications. The demonstrated correlation between molecular geometry, applied field, and toroidal moment provides a computational pathway for designing tunable magnetoelectric and optically active carbon nanomaterials. Physical sciences/Chemistry Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files supportinginformationToroidalmoment.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 03 Dec, 2025 Reviews received at journal 01 Dec, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviews received at journal 05 Nov, 2025 Reviewers agreed at journal 05 Nov, 2025 Reviewers invited by journal 02 Nov, 2025 Editor assigned by journal 01 Nov, 2025 Submission checks completed at journal 31 Oct, 2025 First submitted to journal 23 Oct, 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. 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. 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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-7930501","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":543139367,"identity":"dda273d3-420c-49aa-a841-6cbe10b3d67f","order_by":0,"name":"Arkamita 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Their utility as generators of nanoscale toroidal moment is illustrated. Although the molecules lack structural chirality, \n electric field-induced symmetry breaking \nenables coherent scattering from the topologically ordered ions resulting in toroidization of specific states in which \nelectric and magnetic dipole moments intertwine such that both diminish but give rise to a finite toroidal moment, rending the molecule toroidal and magnetoelectric. \nThe toroidal states are identified from the entirety of the ab-initio calculated spectrum by projecting onto toroidal harmonics and evaluating the electric, magnetic, and toroidal dipole moment which clarifies the microscopic origin of toroidization. Experimentally, the toroidal nature of these states entails optical activity which is confirmed by rotary power calculations. \n Importantly, the activated toroidal states are optically achievable with one photon transitions, leading to a toroidal dipole moment which is persistent and can be converted into a pulse of time-dependent toroidal dipole moment by switching off the static electric field. \nFurthermore, topological superatomic molecular orbitals (SAMOs) are discovered with charge distribution outside the fullerene tori and are found to exhibit pronounced toroidal or mixed toroidal–helical character. These new SAMOs provide natural way to generate nanoscale toroidal electromagnetic field and to induce optical activation of the enclosed valence states. Our findings provide a quantitative framework linking topology, orbital symmetry, toroidal response, and spectroscopic signatures in molecular tori.\nThe results of the microscopic simulations and analysis are experimentally assessable by circular dichroism and have potential applications as further tools in optical control, field-driven manipulation, doping-induced chirality, and quantum information applications. 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