Spin-orbit coupling effects in two-dimensional circular quantum rings: Elliptical deformation of confined electron density

We study electron states confined in two-dimensional circular quantum rings in the presence of spin-orbit coupling due to both structure and crystal inversion asymmetry in the external magnetic field. It is demonstrated that the confined electron density loses the circular symmetry of the confinement potential provided that both Rashba and Dresselhaus coupling constants are nonzero, with the exception of a special case of equal coupling constants and absence of the spin Zeeman interaction. An elliptical deviation from the circular symmetry-present already for a single confined electron-is for two electrons strengthened by the Coulomb repulsion. We discuss signatures of the charge-density deformation in the experimentally accessible quantities: magnetization and charging properties of the ring. Relevance of the results of one-dimensional ring models for description of spin-orbit coupling effects is also discussed.