Quantum rings: Electronic properties

Abstract

We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We write the Schrödinger equation and use the thin-layer quantization procedure to calculate the wavefunctions and the energy spectrum. In such a procedure, it arises a geometry-induced potential, which depends on both the mean and the Gaussian curvatures. Nevertheless, since we consider a ring with a mesoscopic size, the effects of the Gaussian curvature on the energy spectrum are negligible. The magnetization and the persistent current are analyzed. We observed the Aharonov–Bohm (AB) type oscillations. The finite ring width has a fundamental role in the oscillatory behavior found in physical properties as a function of the magnetic field. In general, the role of curvature is to increase the amplitude of oscillations. Nevertheless, in a system with few electrons, an adequate choice of the parameters a1 and a2 allows for observing the effect of the geometric potential on the physical properties.