Bound states of Dirac electrons in a graphene-based magnetic quantum dot

We investigate the magnetically confined states of the massless Dirac fermions in a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the dot. The calculated energy spectrum exhibits quite different features with and without the magnetic field inside the dot. It is found that the degeneracy of the relativistic Landau level with negative angular momenta can be lifted, and this degeneracy breaking can be modulated by the magnetic field inside the dot. Moreover, such a system can form the strongly localized states within the dot and along its boundary, especially with the magnetic field inside the dot.