Dipole and solenoidal magnetic moments of electronic surface currents on toroidal nanostructures

The time-dependent Schr?dinger equation is developed for a spinless electron which is confined to move on a toroidal surface and curvature effects are taken into account. The electron motion is driven by linearly or circularly polarized microwaves including an interference field. To calculate the magnetic moments which are induced by the electronic surface currents on the torus an eight-state basis set is used. The system is driven at a resonance frequency to allow for transitions between states with opposite θ-parity. Optical transitions into modes of excitation can be observed that correspond to a magnetic dipole term parallel to the toroidal central symmetry axis as well as additional components in radial and azimuthal direction (solenoidal modes). Size and relative magnitude of the different components can be steered by adjusting magnitude, polarization, and phase information of the microwave field. Substantial enhancements of the solenoidal magnetic modes versus the dipole mode can be observed when adding a sufficiently strong static magnetic field parallel to the symmetry axis.