Voltage-driven ring confinement in a graphene sheet: assessing conditions for bound state solutions.

We have systematically studied the single-particle states in quantum rings produced by a set of concentric circular gates over a graphene sheet placed on a substrate. The resulting potential profiles and the interaction between the graphene layer and the substrate are considered within the Dirac Hamiltonian in the framework of the envelope function approximation. Our simulations allow microscopic mapping of the character of the electron and hole quasi-particle solutions according to the applied voltage. General conditions to control and operate the bound state solutions are described as functions of external and controllable parameters that will determine the optical properties ranging from metallic to semiconductor phases. Contrasting behaviors are obtained when comparing the results for repulsive and attractive voltages as well as for variation of the relative strength of the graphene-substrate coupling parameter.

Anisotropy induced localization of pseudo-relativistic spin states in graphene double quantum wire structures.

We study the single-particle properties of Dirac Fermions confined to a double quantum wire system based on graphene. We map out the spatial regions where electrons in a given subband display the largest occupation probability induced by spatial anisotropic effects associated to the interaction strength between the graphene wires and the substrate. Here, the graphene-substrate interaction is considered as an ad hoc parameter which destroys the zero-gap observed in the relativistic Dirac cone characteristic of graphene electronic energy dispersions. Furthermore, the results indicate that the character of quasi-extended spin states, viewed by multisubband probability density function, is highly sensitive to spatial asymmetries and to the graphene-substrate interaction strength.