Quantização de Landau, magnetização e correntes persistentes em um anel bidimensional no espaço curvo

Abstract

In this study, we investigated the moviment of a electron confined to a 2D ring in the presence of a uniform magnetic field and an Aharonov-Bohm (AB) field through the center of the ring. The ring is defined by a radial potential. We do not take into account the electron spin. The ring is immersed in a curved surface, which is chosen as the surface of a cone. The dynamics of the system is governed by the Schrödinger equation of motion in curved space. As a result of the geometry model, called the geometric potential arises. This geometric potential is given in terms of the mean and Gaussian curvatures. The latter presents a singularity at region r = 0. The potential that defines the ring is inserted into the Schrödinger equation via coupling vector. The wave functions and the energy eigenvalues are calculated. From these two results we studied how the curvature of the surface, as well as the magnetic fields influence the characteristics of an electron confined to a geometry of a 2D ring. In the same context, we studied the magnetization and the persistent current. Finally, we studied the properties of the main limiting cases derived from the potential of the ring model, such as 2D quantum wire, a quantum ring 1D, the quantum dot and the quantum anti-section.