Odd–even width effect on persistent current in zigzag hexagonal graphene rings

Abstract

The electronic structure and thus the persistent current of zigzag hexagonal graphene rings are investigated within the tight-binding formalism. The flux-dependent energy spectrum is grouped into bands with six levels per band due to inter-valley scattering at the corners of the ring. It is found that the degeneracy at the Fermi level is determined by the even or odd quality of the ring width N. The sample ring becomes metallic at odd N but semiconducting at even N, showing up a strange odd–even width effect. In metallic rings, the persistent current within a flux period is linearly changed with magnetic fluxϕ, while it is a sinusoidal periodical function of ϕ in semiconducting rings. In addition, with increasing N, the persistent current exponentially decreases (increases) at odd (even) N, but finally falls into the consistence with each other at enough large N, showing that the odd–even effect may be experimentally observable only in narrow rings.