Geometric variations and magnetic field effects on electron energy states of InAs/GaAs quantum rings

We study electron energy states in three-dimensional (3D) narrow-gap semiconductor quantum rings with ellipsoidal-shape torus (EST) and cut-bottom EST (CBEST) under an applied magnetic field. Our model includes the effective one-electronic-band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary condition. It is solved by the nonlinear iterative method to obtain a "self-consistent" solution numerically. The electron energy dependence on the inner radius, height, and lateral width is investigated for InAs/GaAs quantum rings with EST and CBEST shapes. The height and lateral width play a crucial role in varying the energy spectra of the rings. When the magnetic field is applied on a fixed-size CBEST ring, we find that there is a nonperiodical transition among the lowest electron energy states. Compared with the well-known 1D Aharonov-Bohm periodical oscillation, the electron energy levels increase and oscillate nonperiodically when the magnetic field is increased. Our calculation for single-electron magnetization shows that the magnetization is nonperiodical and is a negative function of magnetic field.