Electronic structures in a CdSe spherical quantum dot in a magnetic field: Diagonalization method and variational method

Abstract

The electronic structures of a CdSe spherical quantum dot in a magnetic field are obtained by using an exact diagonalization method and a variational method within the effective-mass approximation. The dependences of the energies and wave functions of electron states, exciton binding energy, exciton transition energy, and exciton diamagnetic shift on the applied magnetic field are investigated theoretically in detail. It is observed that the degeneracy of magnetic quantum number m is removed due to the Zeeman effect when the magnetic field is present. For the states with m ≥ 0, the electron energies increase as the magnetic field increases. However, for the states with m < 0, the electron energies decrease to a minimum, and then increase with increasing the magnetic field. The energies and wave functions of electron states obtained from the variational method based on the variational functions we proposed are in excellent agreement with the results obtained from the exact diagonalization method we presented. A comparison between the results obtained from the variational functions proposed by us and Xiao is also verified.