Confined electronic states and their modulations in graphene nanorings

Confined electronic states in quantum rings formed by spatially modulated finite Dirac gap (FDGQR) in graphene are systematically studied by series-expansion method, and are compared with those in infinite-mass-boundary and one-dimensional quantum rings. The shape-size effect of FDGQR is illustrated to be distinct from that in graphene quantum dots. The Aharonov-Bohm effect in FDGQR is clearly shown by the energy spectrum and the optical-transition probabilities. The FDGQR coupled with the electrostatic-potential induced nanoring is found useful for modulating the Dirac electronic states and the optical-transition probabilities. These results may help us to understand and to control the quantum behaviors of confined electronic states in graphene.