The dipolar coupling of two edges of a metallic ring is well known to lead to two plasmon modes, say symmetric and antisymmetric modes. Varying the wall thickness will essentially make changes to these two modes. On decreasing the wall thickness, the excitation energies of a symmetric mode will increase, whereas those of an antisymmetric mode will decrease. The question arises: "What about the coupling effect in graphene rings?" As a 2D electron system with a relatively smaller electron concentration than a 3D metal, the coupling effects in graphene rings might behave differently. In J. Phys.: Condens. Matter 24 402202, we use a quasistatic approach and 3D full-wave simulations to investigate the plasmon energies as a function of the ratio a (the radii of the inner hole over the outer disk).

In the quasistatic approach, we develop a self-consistent integral equation for the scalar potential or induced charge density. The numerical solutions of this equation show that the antisymmetric plasmon modes have a resonance dip as a function of the ratio a. This differs from the response of other structures such as metallic rings.

This unusual phenomenon in graphene rings is determined by the different coupling strengths of the two edges. It is weakly coupled at smaller a, and strongly coupled at larger a. In the weakly coupled regime, the plasmon resonances can be considered as an inner hole and an entire disk, so energies of the antisymmetric mode will decrease as a increases. However, in the strongly coupled regime, they are hybridized and the energies of the antisymmetric mode are proportional to the coupling strengths. Our numeric investigations show that the transition point is at a = 0.25, and satisfies the electrostatic scaling law, for instance. The finding is confirmed by the COMSOL simulations for both micron and nano graphene rings.