Spin-Orbit Energy State Splitting in Semiconductor Cylindrical and Spherical Quantum Dots

Abstract

We present a theoretical study of the spin-orbit interaction impact on electron energy states in small cylindrical and spherical quantum dots. The investigation is based on the effective one-electronic band Hamiltonian and the spin dependent boundary conditions. It has been demonstrated that the spin-orbit interaction can significantly modify the energy spectrum of InAs and InSb quantum dots. The splitting can provide a situation where only the lowest spin split energy states are bound in the dot. A reasonable agreement was found with data from more sophisticated theoretical models for the spherical quantum dots which is available in the literature.

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

“…It can be further transformed into a form where the spin dependence only dwells in the boundary conditions [6], [14] resulting in two Schrödinger equations which differ only on the interface conditions between the quantum dot and the surrounding bulk material. Numerical experiments demonstrating the influence of the spin-orbit splitting on the relevant energy levels for rotationally symmetric quantum dots are contained in [9], [10], [15], [16], [17], where the Schrödinger equations are discretized by finite differences, and the resulting nonlinear eigenproblem is solved by the full approximation method.…”