Influence of electric fields on magnetization of achiral carbon tori

Energy gap (Eg) of achiral carbon tori in electric (F) and magnetic (B) fields is studied within the tight-binding model including the curvature effect. It has strong dependence on the direction and the magnitude of B. The Zeeman effect causes zero-gap transitions (Eg≠0→Eg=0) (ZGTs) to happen more frequently. Moreover, the perpendicular electric field (F⊥) could further affect the positions and times of the ZGT occurrence and the width of Eg. ZGTs make magnetization (M) exhibit special jump structures (SJSs) at zero temperature. Magnitude of M and magnetism are mainly determined by the angle (αB) between B and the symmetric axis. For armchair carbon tori, M exhibits many SJSs and shows paramagnetism at αB>30∘. Furthermore, F⊥ strongly affects the features of SJS and change the magnetism at larger αBʹs. Contrarily, SJS is absent and M shows paramagnetism at any αBʹs for zigzag carbon tori. Additionally, modulation of magnetization by F is very different for various kinds of armchair carbon tori. The differences include the magnitude of M and the existence of a single SJS or pair of SJS.