Propriedades eletrônicas em nanoestruturas de bicamada de grafeno

Abstract

In this work, we investigate the electronic properties in bilayer graphene quantum dot and quantum ring (BLG QDs and QRs, respectively), considering both the usual stacking between the layers, i.e. the so-called Bernal AB type, and the stackings resulting from effective rotations between layers, which lead to the formation of interference patterns known as moiré patterns. In the first study, which considers the usual stacking (AB type), we systematically analyze the energy levels and probability densities for the π band eléctrons in BLG QRs. The nanostructures were defined for different geometries, edge types, and arrangements between the inner and outer edges. Additionally, we investigate how the energy levels are modified by the inclusion of a homogeneous magnetic field perpendicular to the plane of the rings. For this, we use a tight-binding model for first neighbors, and the numerical results were compared with those from the literature on graphene QDs in both monolayer and bilayer configurations, as well as graphene QRs in monolayer, highlighting the electronic similarities and differences between these structures. Next, in the second study, we address the electronic behavior in QDs and QRs in twisted bilayer graphene (tBLG) under the influence of a perpendicular magnetic field. Our results indicate that, for rotation angles θ close to 0◦ or 60◦, the energy spectra exhibit features originating from the interaction of AA and AB/BA stacking orders, responsible for the formation of the moiré pattern in tBLG. For rotation angles between 10◦ and 50◦, the low-energy levels are found to be practically independent of the rotation angle. In the absence of a magnetic field, the energy levels of the QRs follow a power law as a function of the ring width, with the exponent varying from 1 to 2, depending on the rotation angle. Even more interestingly, the lowest energy states of the tBLG QRs oscillate as a function of the average radius Rm, with an oscillation period that approximately coincides with half the moiré period. When an intense magnetic field is applied, the lowest energy levels in the tBLG QDs and QRs align almost identically, regardless of whether the outer radius of the quantum confinement structure is smaller than or equivalent to the moiré period. This phenomenon can be attributed to the interlayer between the trigonal warping effect and the preferred location of the eigenstates. Our results provide valuable insights into the moiré pattern in tBLG and its role in the confinement of charged particles. Both studies developed in this thesis elucidate the electronic properties in BLG with great potential for applications in optoelectronic devices.