Sobre propriedades físicas em anéis quânticos no grafeno

Abstract

In this work, we study the graphene and its physical properties associated with the theory of the topological defects in solids of Katanaev and Volovick, mainly the kind of topological defect known in the literature as disclination, obtained through the Volterra process. Graphene is a two-dimensional crystalline (2-D) semiconductor material with null gap in which, for the low energy regime, the energy dispersion relation is linear and the charge carriers behave as particles of half-integer spin, fermions , whose dynamics is described by the Dirac equation. We also discuss the behavior of charge carriers in graphene in two situations: massless fermions and massive fermions. The latter is related to the effective mass behavior that arises with increasing separation of the gap between the conduction and valence bands in the bands structures, known as gapped graphene. However, there is the problem of electronic confinement in this type of material because of quantum tunneling. An alternative to this question is the relativistic extension of Tan Inkson’s (2-D) quantum ring model proposed by Bakke and Furtado, based on the Dirac oscillator. From this coupling, in the first part of this work, the energy spectrum, the persistent currents, and the positive spinors were obtained for a non-massive graphene sheet with/without topological defect disclination, by Dirac equation (2+1) dimensions, in the presence of Aharonov-Bohm flux. The second part, we consider the addition of magnetic field vertical to the plane of the gapped graphene sheet, where we get besides all the concepts already mentioned, the magnetization of this system. Finally, the third step of this work, we consider the rotation of this system, in order to investigate the non-inertial effects on graphene which has been subjected to disclination and the ringed confinement.