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

Abstract

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

“…1 This interference phenomenon is associated with persistent currents and magnetization, and its strength can be modulated by tailoring the shape and the size of the QR. 2 In particular, semiconductor QRs have been the subject of intense experimental [3][4][5][6][7][8][9] and theoretical [10][11][12][13][14][15][16][17] works. The simplest model of a quantum ring has a circular shape and uniform width.…”

“…Recently, we calculated the electronic states of thin QRs with arbitrary ͑but smooth͒ variations in curvature and width and reported numerical results for elliptical rings. 13 Since the thinner regions of a ring are less favorable for the electron, we were able to obtain a width profile that compensates for the effects of the non-uniform curvature of the ellipse.…”