The Effect of External Magnetic Field on the Creation of Energy Levels Degeneracy in a Quantum Anti-Dot

In this paper, the effect of a magnetic field on 2p energy levels of 〖Ga〗_(1-x) 〖Al〗_x As/GaAs/〖Ga〗_(1-x) 〖Al〗_x As quantum anti-dot has been investigated. To this aim, based on the perturbation theory and in the presence of an external magnetic field, the energy eigenvalue of the 2p state of this nano-structure is obtained. Then, on the basis of theoretical predictions and numerical calculations, it will be shown that the magnetic field does not always eliminate the degeneracies of energy levels and under certain conditions, the magnetic field itself is the cause of a new degeneracy in the energy levels. Furthermore, it is proved that changes in the height of the potential barrier will remove the degeneracy created after the application of the magnetic field.