The effects of inner radius and width on the energy spectrum and persistent current in zigzag hexagonal graphene quantum rings

In this work, the effects of inner radius and width variation on energy spectrum and persistent current in hexagonal graphene quantum rings with zigzag edges have been studied by using the tight-binding model. Our investigation show that the energy spectra of these rings are grouped into subbands which each one consists of six coupled energy levels that separated by energy gaps. The pattern of these subbands and gaps are strongly affected by inner radius and width. In other words, width and inner radius of the HGRs plays a very important role in gap engineering. Narrow HGRs have more regular energy subband patterns and also larger gaps, which is due to increasing the quantum confinement and the edge effects, especially in the corners of the structure. Increasing the inner radius leads to the compression of six coupled energy levels in each subbands therewith decreasing the subband gap near the Fermi level. Furthermore, increasing the inner radius or width have similar effects on the energy spectrum, so the effect of increasing one of them can be neutralized by decreasing the other one. Specially, it is dominant for the energy gap near the Fermi level. Additionally, increasing the inner radius or width leads to increasing in the amplitude and oscillations of persistent current versus magnetic flux. Meanwhile, width variation is more effective than variation of inner radius on persistent current.