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Chinese Journal of Physics

Aharonov-Bohm Effect on Landau States in Annular Cylindrical Boxes

E. Ley‐Koo, G. Villa‐Torres, Dmitrii Kouznetsov

Published Apr 1, 2002• 3 citations
OpenAlex

Abstract

The Schrodinger equation for an electron inside an annular cylindrical box and in the presence of an axial uniform magnetic field is solved in two comparative situations: i) when the magnetic induction ~ B0 = kB0 is the same in the central perforation and in the box, and ii) when its values in the perforation ~ Bi = kBi and in the box ~ B0 = kB0 are different. The Aharonov-Bohm effect on the Landau states of the confined electron is exhibited through the analysis of the dependence of the energy eigenvalues and eigenfunctions on the difference of the magnetic flux in the perforation as B i i B0 changes.

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The Schrodinger equation for an electron inside an annular cylindrical box and in the presence of an axial uniform magnetic field is solved in two comparative situations: i) when the magnetic induction ~ B0 = kB0 is the same in the central perforation and in the box, and ii) when its values in the perforation ~ Bi = kBi and in the box ~ B0 = kB0 are different. The Aharonov-Bohm effect on the Landau states of the confined electron is exhibited through the analysis of the dependence of the energy eigenvalues and eigenfunctions on the difference of the magnetic flux in the perforation as B i i B0 changes.
An asymptotic formula for the energy eigenvalues of a charged particle contained in a cylindrical shell is derived. The formula is used to estimate the eigenvalues when there is a cylindrically symmetric static magnetic-induction field present and the system exhibits the bound-state Aharonov-Bohm effect. It is shown that the errors involved form an sequence with terms labelled by the radial quantum number. Numerical approximations obtained from the asymptotic formula are compared to those obtained from analytical solutions of Schrödinger's equation in the following two cases. (i) There is no magnetic-induction field in the shell itself but there is a field inside the inner cylinder. (ii) There is a constant magnetic-induction field in the shell as well as a (possibly different) field inside the inner cylinder. In these cases, the radial eigenfunctions are expressible in terms of Bessel functions and confluent hypergeometric functions, respectively. The numerical results are consistent with the asymptotic character of the formula for the energy eigenvalues.
In this paper, we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the presence of an Aharonov–Bohm flux and a uniform magnetic field, we solve the Schrödinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.
This work presents an analysis of the Aharonov-Bohm effect taking into account both regions where the electron is present and where it is excluded, and also the time variations of the magnetic vector potential and the magnetic induction field as they change between two of their stationary values. This analysis allows the identification of the electrical force field induced in the region where the electron is present by the time variation of the magnetic flux in the region where the electron is excluded, thus providing a classical explanation of the changes in the stationary properties of the electron when the magnetic potential and field change from one set of stationary values to another. Some apparent contradictions in attempts to interpret the A-B effect are also discussed and clarified.
Abstract In this work, we solve the Schrödinger equation of a particle restricted to move on a cone surface of finite height under the influence of an Aharonov–Bohm magnetic field. The energy eigenvalues and their respective wave functions are obtained analytically as a function of the radial distance from the apex and the apex angle. We compute the Shannon entropy in configuration and momentum space for the ground and the first excited states as a function of the slant height and the apex angle. In the absence of magnetic flux the states (n,m) and (n,−m) have identical Shannon entropies, but for non-zero fluxes the Shannon entropies of these states are different, their values depending on the state, the apex angle and the value of the magnetic flux.