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

Abstract

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 Schrödinger 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 limaçon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations. © 2008 The American Physical Society.