Magnetic field dependence of electron energy states in 3D nano-scopic quantum rings

We study theoretically the electron energy states for realistic models in 3D nano-scopic semiconductor quantum rings. The effective one-band Hamiltonian approximation and the Ben Daniel-Duke boundary conditions are considered simultaneously in the model formulation. The proposed model problem is solved numerically by using central difference scheme with non-uniform meshing technique, shifted and balanced QR algorithm, and inverse iteration method. It is found that calculation results strongly depend on the radial cross shapes of InAs/GaAs quantum rings. The dependence of energy states on an external magnetic field for 3D nano-scopic quantum ring indicates there is a significant difference among those reported results with simplified 1D or 2D approaches in literature. Simulation results demonstrate very good consistence with the experimental data.