Band strutures of hybrid graphene quantum dots with magnetic flux

We study the band structures of hybrid graphene quantum dots subject to a magnetic flux and electrostatic potential. The system is consisting of a circular single layer graphene surrounded by an infinite bilayer graphene. By solving the Dirac equation we obtain the solution of the energy spectrum in two regions. For the valley $K$, it is found that the magnetic flux strongly acts by decreasing the gap and shifting energy levels away from zero radius with some oscillations, which are note observed for null flux case. As for the valley $K'$, the energy levels rapidly increase when the radius increases. A number of oscillations appeared that is strongly dependent on the values taken by the magnetic flux.