Electronic states in quantum rings: electric field and eccentricity effects

The polarization effects of in-plane electric fields and eccentricity on electronic and optical properties of semiconductor quantum rings (QRs) are discussed within the effective-mass approximation. As eccentric rings may appropriately describe real (grown or fabricated) QRs, their energy spectrum is studied. The interplay between applied electric fields and eccentricity is analysed, and their polarization effects are found to compensate for appropriate values of eccentricity and field intensity. The importance of applied fields in tailoring the properties of different nanoscale materials and structures is stressed.

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

Quantum rings of arbitrary shape and non-uniform width in a threading magnetic field

The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schrodinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and limacon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations.

Aharonov-Bohm oscillations in a quantum ring: Eccentricity and electric-field effects

The effects of an in-plane electric field and eccentricity on the electronic spectrum of a GaAs quantum ring in a perpendicular magnetic field are studied. The effective-mass equation is solved by two different methods: an adiabatic approximation and a diagonalization procedure after a conformal mapping. It is shown that the electric field and the eccentricity may suppress the Aharonov-Bohm oscillations of the lower energy levels. Simple expressions for the threshold energy and the number of flat energy bands are found. In the case of a thin and eccentric ring, the intensity of a critical field which compensates the main effects of eccentricity is determined. The energy spectra are found in qualitative agreement with previous experimental and theoretical works on anisotropic rings.