Geometry dependence of persistent currents in diamond-like graphene rings

The electronic structures and the persistent currents of diamond-like graphene rings (DGRs) are investigated within the tight-binding formalism. The calculations show that an armchair DGR is a metallic ring only at selected ring width N = 3 m − 1 ( m is an integer), while a zigzag one appears to be metallic regardless of its geometry. The persistent currents in DGRs are calculated, depending strongly on their geometries. It is found that the persistent current in a metallic armchair DGR is near an order of magnitude larger than that in a metallic zigzag hexagonal graphene ring (HGR) of equivalent size [M.M. Ma, J.W. Ding, N. Xu, Nanoscale 1 (2009) 387]. In the metallic zigzag DGRs, the persistent currents are declined generally by two orders of magnitude compared with the sizable metallic armchair DGRs.