Circumferential confinement consequence on the magnetic properties of a punctured nanotube in the presence of an axial electric field

In this paper, we present magnetic properties of a finite graphene sheet with a triangle punctured vacancy, and its counterpart single-wall carbon nanotube as a rolled-up graphene sheet in the framework of the Hubbard model in the presence of an axial electric field, in order to form a comparison study between these two graphene samples. We have noticed that the tight-binding part of the Hamiltonian consists of two types of zero-energy states in the case of the graphene sheet, the strict zero-energy states, and the quasi zero-energy states. The first type takes part in a ferromagnetic coupling between the triangle edges and one edge of the rectangle graphene sheet, while the latter one has an antiferromagnetic alignment with the opposite edge of the rectangle graphene sheet. Involving the Coulomb interaction through Hubbard term, we have observed that the slope of the cluster edge states in nanotube is higher than the graphene sheet. Additionally, spin-depolarization happens in single-wall nanotube sooner than the graphene sheet by slightly increasing an axial electric field. Also, the graphene sheet is more robust than the single wall nanotube at low electric fields. (paper)