Computer simulation of electron energy state spin-splitting in nanoscale InAs/GaAs semiconductor quantum rings

In this paper, we model and computationally investigate the effect of spin-orbit interaction on the electron energy spectra for nanoscale semiconductor quantum rings. Our three-dimensional mathematical model considers the effective one-electron band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the spin-dependent Ben Daniel-Duke boundary conditions. The nonlinear iterative method is applied to solve the corresponding nonlinear eigenvalue problem, which converges monotonically for all energy states. Physically, it is found that the spin-dependent boundary conditions lead to a spin-splitting of the electron energy states with non-zero angular momentum in nanoscale InAs/GaAs quantum rings. The spin-splitting is strongly dependent upon the dimension of the explored quantum ring and is dominated by the inner radius, the base radius, and the height of the quantum ring. Under zero magnetic fields, the spin-splitting energy is decreased when the radius is increased. Meanwhile, it is greater than that of the InAs/GaAs quantum dot and demonstrates an experimentally measurable quantity (up to 2 meV) for relatively small semiconductor quantum rings.