Study On The Persistent Currents In Mesoscopic Graphene Rings

Based on the tight-binding model, the eigenstates and persistent currents of electrons in simple nanotubes, mesoscopic M?bius rings and mesoscopic graphene rings are theoretically studied.(1) The energy spectrum and persistent currents of simple nanotubes and mesoscopic M?bius rings are studied analytically and numerically. Specially, we need to disscuss the parity of the width of the mesoscopic M?bius rings to obtain the energy spectrum of them. Some new phenomenon and consequence are found about persistent currents of simple nanotubes and mesoscopic M?bius rings. The persistent currents change with the magnetic flux linearly or sinusoidally when the geometric parameters of the systems meet some special relationship.(2) The energy spectrum and persistent currents of mesoscopic graphene rings with armchair and zigzag edges are studied analytically and numerically. The characters of persistent currents changing with Aharonov-Bohm(A-B) magnetic flux in rings with different geometry are investigated thoroughly. The periodicity and special symmetry of energy spectrum and persistent currents changing with the magnetic flux are revealed. It is demonstrated that the persistent currents are determined by the geometric structures of rings. For mesoscopic graphene rings with armchair edges, the quantum states with small eigen-energies carry much larger currents than those quantum states with eigen-energies far away from zero. However, mesoscopic graphene rings with zigzag edges have two kinds of electronic states, i.e., the standing state and edge state; and persistent currents of them are different from graphene rings with armchair edges.