Single-particle electronic spectra of quantum rings: a comparative study

The single-particle electronic spectra of semiconductor self-assembled quantum rings are theoretically analyzed. We studied two different models for the lateral confining potential: the displaced parabola (Hill) and the centrifugal-like core (Volcano). The corresponding energy levels are systematically analyzed as a function both of the ring radius, and external magnetic fields perpendicular to the ring plane. The one-electron ground state of the Hill potential presents an absolute minimum when studied as a function of the ring radius. Numerically exact and approximate solutions are compared for the case of the Hill ring. Each one of the two ring models leads to a characteristic level crossing pattern in the presence of a perpendicular magnetic field, which can be used to identify which of both models is more suitable to fit one-electron spectroscopic data. The electronic spectrum of elliptical Hill rings, with broken azimuthal symmetry, is also presented. It is found that the Hill confinement potential provides a more suitable theoretical description of nanoscopic semiconductor self-assembled rings than the Volcano confinement.