Effect of external fields on low-frequency optical properties of achiral carbon tori.

By using the tight-binding model including the curvature effect, the low-frequency electronic and optical properties with perpendicular polarization under electric and magnetic fields are studied for achiral carbon tori. Electronic properties (state energies, energy gaps, state degeneracy and wavefunctions) are strongly modulated by varying the direction and the magnitude of electric fields. The perpendicular magnetic field further enhances modulations of the electronic states. The variation of state energies and wavefunctions with external fields could be directly reflected in optical properties such as the amplitude and the frequency of absorption spectra and the exhibition of new peaks. Additionally, dependences of the low-frequency absorption peaks on electric fields, with and without magnetic fields, are significantly sensitive to the toroidal geometry.