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arXiv:1908.09956 · International Journal of Geometric Methods in Modern Physics

A quantum ring in a nanosphere

A.L. Silva Netto, B. Farias, J. Carvalho, Claudio Furtado

Published Aug 20, 2019• 10 citations
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Abstract

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.

DOI
10.1142/s0219887819501676

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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.
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.
Aharonov-Bohm ring (AB ring) is an element frequently used in nanosystems.The paper deals with wave dynamics on quantum graph consisting of AB ring coupled to a segment.It is assumed that the lengths of the edges vary in time.Variable replacement is made to come to the problem for stationary geometric graph.The obtained equation is solved using the expansion with respect to a complete system of eigenfunctions of the unperturbed self-adjoint operator for the stationary graph.The coefficients of the expansion are found as solutions of a system of differential equations numerically.The influence of the magnetic field is studied.The comparison with the case of stable geometric graph is made.
We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.
Electron spin transport through an Aharonov–Bohm ring driven by time-dependent inhomogeneous magnetic fields is treated. The system possesses an su (2) l × su (2) s dynamical symmetry in both orbital angular momentum space and spin space, and is thus proved to be integrable according to algebraic dynamics. Based on the analytical solutions, the relevant physical quantities such as electric current, spin current, magnetization and conductance are calculated. It is found that for a magnetic field with π/2 twist angle, the direction of spin-polarization will be reversed at zero magnetic flux. In the resonant rotating magnetic field, the spin transmission is oscillating with time t , and can reach unity, so that a complete spin flip can also be induced. The results obtained may be of practical significance for the design of nano-electromagnetic spin devices, such as a spin switch, in a controllable way.
The two-dimensional solution of the spinless Klein–Gordon (KG) equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB) flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU) method. The exact energy eigenvalues and normalized wave functions are analytically obtained in terms of potential parameters, magnetic field strength, AB flux field and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0) and AB flux field (ξ = 0) case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.