Chiralność w układach wielowarstwowych grafen, heksagonalny azotek boru
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Discovery and manufacturing of a graphene, new two dimensional material, begun the period of research on the topologically flat surfaces. It turned out that the two dimensional structures, especially the graphene, have properties which make them excellent candidates for use in electronics and making research in the field of relativistic quantum mechanics. Graphene, not being influenced by any other material, doesn’t have a band gap and effective mass of charge carriers is equal to zero. Due to these properties one can classify graphene as a semiconductor with linear dispersion. These ideal properties are changed while attempting to build the physical electronic device, as an effect of interaction with substrate. One of the best commonly used substrate for graphene is a hexagonal boron nitride (h-BN). This two dimensional material with the structure of the honeycomb has a lattice constant very similar to the graphene’s lattice constant. Moreover it is more flat in comparison with others materials which can serve as a substrate. Summing up the hexagonal boron nitride is a perfect candidate for electronic devices based on graphene, since as a substrate it doesn’t influence the electronic structure of graphene much. Up to this moment this was the main use of the h-BN in two dimensional electronic devices. Due to the specific properties of h-BN I decided to make the research in which I ask how with the use of h-BN it is possible to model the electronic structure of graphene multilayers. In order to do this I broadened the procedure of chiral division, used commonly for the multilayers of graphene to the multilayers consisting of graphene and hexagonal boron nitride. Analyze of the electronic properties of examined multilayers in dependence of the position of h-BN and graphene shows that h-BN can be an active modeling factor. That is being an insulator is only one of the properties for which we can use h-BN layer. Most intriguing are graphene/h-BN/graphene multilayers with the odd number of graphene monolayers on the both side of h-BN. In such system one can distinguish subsystem with the linear dispersion and zero gap band. This means in such system there exist free graphene monolayer. Moreover in my thesis I made a research on the Klein tunneling the phenomenon known from the quantum field theory. My research provide the description of tunneling in the bilayer graphene in the four band approach and gives the description of the Klein tunneling in the cases of hybrid structures consisting of graphene and h-BN. Described in my thesis multimode tunneling can have a practical implication in construction of the electronical devices especially the IFET (inter layer field effect transistor) devices.