Hydrogenic impurity states in a spherical quantum antidot: Spin-orbit interaction, relativistic correction, and diamagnetic susceptibility

In the present work, we study three characteristics of a hydrogenic impurity located at the center of a GaAs/Ga1-xAlxAs spherical quantum antidot within the effective mass approximation. These characteristics are the diamagnetic susceptibility, the spin-orbit interaction (SOI), and the relativistic correction (RC). First we outline the analytic solution of the corresponding Shrodinger equation with a hydrogenic impurity at the center and obtain the energy levels and wave functions. The results obtained from the present work reveal that the diamagnetic susceptibility increases with increasing the antidot size for finite barrier. The mean value of r(2) increases when the antidot size increases. The SOI and RC increase by increasing the concentration. The RC and SOI approach to zero when the antidot size increases. The splitting between j = 1/2 and 3/2 due to the SOI decreases by increasing antidot size.