Variational calculations on the energy levels of graphene quantum antidots

Abstract

Within the Dirac-Weyl description of the graphene, the ground and low-lying excited state energies of a graphene quantum antidot subjected to a uniform static magnetic field is calculated by employing a variational scheme. The procedure is based on the choice of exact solutions of the Dirac-Weyl equation corresponding to massless fermions under the homogeneous magnetic field as basis sets for the trial wave functions. It is found that, for parabolic graphene antidots, the valley splitting occurs due to the introduction of spatial confinement, and it increases as the confinement strength increases. Furthermore, it is also investigated that, in such dot structures, switching an antidot potential on enhances this splitting. Therefore, we investigated that it is possible to control valley splitting by geometrical parameters of a graphene quantum antidot and/or by the strength of external magnetic field.