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

Abstract

The time-dependent Schrödinger 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.

Quantum electron transport in toroidal carbon nanotubes with metallic leads

“…the torus lieing flat on the two planar leads will allow an increase in the number of metal-carbon contact sites and possibly lead to better and closer lead attachment. This could prove to be very interesting in the context of an applied microwave field with an additionally tilted static magnetic field due to the interplay between electronic excitations and persistent and bias-driven currents through the torus [40,41,42]. It is conceivable that quantum control applications could follow when the induced dipole and solenoidal magnetic moments couple to electronic spin.…”

“…To date, most of the efforts directed towards quantum rings have focused on flat two-dimensional structures [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. While these objects can be more easily modelled in comparison to their toroidal counter parts, toroidal structures allow for motions around their minor radius in addition to azimuthal motion, which could give rise to novel phenomena [40,41,42]. Some of the potential applications by which the unique transport features of nanoscale tori might be exploited are:…”

Toroidal moments of Schrödinger eigenstates

“…However, to include the curvature potential as a function of λ, it would be necessary to find φ(λ) along the curve. While this could be accomplished numerically, using the azimuthal angle is somewhat better suited to incorporating external fields [29,30].…”

Efficient Toroidal Formation of Sorted Metallic and Semiconducting Single-Walled Carbon Nanotubes via General Pickering Emulsion

“…Many studies have been conducted to investigate the structural models of tori CNTs to investigate their thermodynamic stabilities. The work of Ihara et al showed that the tori CNTs are found to be more stable than the C 60 fullerene, comparing the cohesive energies. ,− Additionally, many numerical simulations have demonstrated that the toroidal SWNTs (TSNs) exhibit quantum interference effect in charge transport under an external magnetic field or electromagnetic field, along their potential use as a macroscopic molecular toroid/coil with the molecular Aharonov–Bohm oscillator, spin-polarized current injector, detection of biopolymers, and metal–insulator transition switching. − Recently, gold nanoparticles (Au NPs) were deposited on CNT rings for theragnostic applications . Nevertheless, the experimental studies and applications of TSNs have been dilatory as the theoretical investigations .…”