Topology-enabled quantum toroidal moment in carbon nanotori

Abstract

Beyond conventional electric and magnetic dipoles, toroidal moments represent a distinct class of charge-current distributions that are challenging to realize at the molecular scale. Here, we demonstrate optically active toroidal electronic stationary states in pristine, achiral carbon nanorings and tori (C120, C144, C168) subjected to a static electric field. Field-induced symmetry breaking enables coherent scattering fromthe topologically ordered carbon network, generating states in which electric and magnetic dipoles largely cancel while a finite toroidal dipole emerges, rendering the molecules magnetoelectric. These states are identified across the ab initio spectrum through projection onto analytic toroidal harmonics and evaluation of electric,magnetic, and toroidal multipolemoments. Their toroidal character leads to intrinsic optical activity, confirmed by time-dependent density functional theory calculations of circular dichroism. Notably, the activated toroidal states are accessible via onephoton transitions and sustain a persistent toroidal dipole that can be released as a time-dependent pulse upon removal of the external field. We further uncover topological superatomic molecular orbitals with pronounced toroidal or mixed toroidal–helical character, acting as nanoscale sources of toroidal electromagnetic fields. Our results establish a quantitative link between molecular topology, orbital symmetry, toroidal response, and spectroscopic signatures in fullerene tori.