Spin-orbit splitting in semiconductor quantum dots with a parabolic confinement potential

We present a theoretical study of the effect of spin-orbit interaction on the electron energy spectrum of cylindrical semiconductor quantum dots. The study is based on a simple effective one-band approximation. The dependence of energy levels on parameters of the dots and the applied external magnetic field is studied. Contributions of the bulk inversion asymmetry (the Dresselhaus term) and the system inversion asymmetry (the Rashba term) to the spin splitting of the electron energy states are discussed. The spin splitting of electron states with nonzero angular momentum is demonstrated theoretically for InSb and InAs small quantum dots at zero magnetic field. We find a "crossing" of the electron energy stales with the same angular momentum and different spin polarizations in a nonzero magnetic field.