Confinamento eletrônico em bicamadas de grafeno - Xavier, Leandro Jader Pitombeira (2011)
In this work we calculated the energy levels around the K and the K′ points of the first Brillouin zone in a bilayer graphene when a electrostatic bias is applied between the layers, such that the sign of the confining potential changes across a channel. Such potencial is known as topological confinement. Starting of tight-binding description of graphene, we derived the “Dirac equation” which governs the behavior of charge carriers around the K and K′ points. We solved the “Dirac equation” with the potential bias applied changing along the radial direction. Firstly, we considered that the potential bias changes its sign once. That forms a quantum ring. Secondly, we considered that the potential bias changes its sign twice. That forms two quantum rings concentric. We show that for potential step kink the Dirac equation can be solved analytically. For each potential we show how the energy levels depend of the potential parameters. We include the effect of a smooth kink using numerical methods and we show how the energy levels change. Our results show that it’s possible to confine the charge carriers in such potentials and are in agreement with the literature ones.