Topology-enabled Quantum Toroidal Moment in Carbon Nanotori

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.