Quantum disc plus inverse square potential. An analytical model for two-dimensional quantum rings : study of nonlinear optical properties

Abstract

ABSTRACT: We will here dedicate to investigate the electronic states in quantum disks which are under the combined influence of two different types of confinement profiles: one parabolic type and one originating from the action of a potential that depends inversely on the square of the distance. All this is complemented by the presence of an externally applied magnetic field. It must be said that the inverse square potential appeared as a model for the interaction between particles in the quantum problem of N particles in a parabolic potential and with an additional magnetic field. We will discuss how the inclusion of this kind of potential along with the other two mentioned fields can serve as a fairly direct model for charge carriers states confined in a one dimensional semiconductor quantum ring. We will demonstrate that the corresponding electronic eigenstates from the Schrödinger like effective mass equation in the conduction band can be obtained analytically. Then, with the use of these states so determined we will calculate the linear and nonlinear contributions to the optical absorption coefficients and relative change of refraction index on a system with the above geometry, based on GaAs