Electron energy state spin-orbit splitting in nanoscopic quantum rings

The impact of spin-orbit interaction on the electron energy states in nanoscopic semiconductor quantum dots and rings is studied theoretically. The effective one-band Hamiltonian approximation with the spin-orbit coupling potential is used. It is shown that the spin-orbit interaction can produce a considerable spin splitting of excited electronic states at zero magnetic fields. We investigated changes in the spin splitting when the geometrical structure is gradually changed from a dot-like shape to a ring-like one. It has been found that the completion of the quantum ring geometry leads to the reversing of the splitting sign.