Grafeno multicamadas através de grafos quânticos periódicos: cones de Dirac

Abstract

We study the spectral characterization and Dirac cones, always through periodic quantum graphs, in three situations. Firstly, we model bidimensional honeycomb materials, for instance, Graphene and Boron Nitride. We consider the Dirac operator with more general Robin vertex condition. Secondly, we propose a model for Bernal-stacked (also called AB-stacked) bilayer and trilayer graphene. Considering the Schrödinger operator with the standard Neumann vertex condition, we have obtained the exact expressions of the dispersion relation for these materials. Finally, also considering the Schrödinger operator with Neumann conditions, we propose the modelling of the AA-stacked multilayer graphene (for n any positive integer) and AA-stacked graphite (a 3D model). For n = 2; 3, exact expressions for the dispersion relations were obtained. For n greater than 4, approximations was employed for the study of the Dirac cones