LAUSR

The analytical expressions for the eigenenergies and functions of the graphene quantum dot perpendicularly pierced by the different but parallel magnetic fields inside (B1) and outside (B2) dot have been derived with the ratio of the magnetic field strengths being irreducible rational B2/B1 = p/q. It is numerically found that the curves of eigenenergies consist of the clusters bounded by a series of the two sequential different Landau levels proportional to 2nB2 and 2nB1, respectively. The eigenenergies depend sensitively on the magnetic quantum numbers as well as the ratio of two different magnetic fields. The counting rules for the number of the valleys within the probability density of the wave functions have been established to interpret the interrelationship between the eigenenergies and wave functions. In addition, the crowding-in effect of the wave functions due to the increase of the eigenenergies is revealed.