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 rin… Show more
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
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.
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
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.
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