Electron energy state spin splitting in nanoscale InAs/GaAs semiconductor quantum rings

Abstract

In this paper, we investigate the effect of spin-orbit iteration oil the electron energy spectra for nanoscale semiconductor quantum rings. Our three-dimensional model considers the effective one-electronic hand Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the spin-dependent Bell Daniel-Duke boundary conditions. The nonlinear iterative method is applied to solve the corresponding nonlinear eigenvalue problem, which converges monotonically. 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 quantum ring and is dominated by the inner radius, the base radius, and the height of quantum ring. At zero magnetic field, the spill-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.