Anéis quânticos em mono- e bicamadas de Grafeno - Xavier, Leandro Jader Pitombeira (2016)
One important field of solid-state physics is the investigation of low-dimensional devices, in which the charge carriers motion is confined in one, two or three dimensions. One important class of such systems are quantum rings, they are a natural systems to investigate quantum interference phenomenon in transport properties, Aharonov-Bohm oscillations and persistent currents. On the other hand, graphene, a planar monolayer of carbon atoms arranged on two-dimensional hexagonal lattice, exhibits peculiar properties like a pseudo-relativistic charge carriers behavior nest to the Fermi level and is expected to lead to the development of new devices. In this work, we studied located states in quantum rings in monolayer and bilayer graphene. One known that, due a interaction with substrate, monolayer graphene can develop a mass term in the Dirac-Weyl equation that describes the charge carriers nest to Fermi level. Furthermore, a mass inversion, obtained through defects on the substrate, can confine charge carriers in the interface of sign change. We studied a system where the sign inversion happens along a circle, therefore, forming a ring-like confinement. The electronic dispersion was calculated as a function of the radius of the circular line defect and the intensity of the mass term induced ether analytically, by continuous model, or numerically, through tight-binding model. Our analytical results show very good agreement with the tight-binding ones. Furthermore, the energies levels are weakly dependent on the intensity of mass term. The states are robust in the presence of disorder, in the sense that non-magnetic can not break the valley degeneracy and are immune to backscattering, like topological states. Also was studied the influence of a external magnetic field and, besides the Aharonov-Bohn oscillations, we found that tunning tha magnetic field, on can control the ground state valley. Under a heterogeneously potential bias, one can confine the charge carriers motion in a bilayer graphene, but, besides the conventional confinement, it is possible to define a topological confinement, in which the potential bias reverse the sign on the confinement zone. Analogously to the monolayer ring, we propose a system where that inversion happens in a circular line, therefore, forming a ring-like confinement in bilayer graphene. The electronic dispersion was calculated analytically as a function of the radius of the circular line, the intensity of potential bias and the intensity of a external magnetic field using the continuous model. The states in such system, similar to the monolayer one, are robust to a non-magnetic disorder and a backscattering.