Band Structure and Spatial Localization of Electrons in Twisted Bilayer Graphene Nanoribbons (Bulletin of Pure and Applied Sciences – Physics, 2022)
We have studied the band structure, density of states and spatial localization of  electron in twisted bilayer nanoribbons by means of tight binding calculation. In  Chiral geometries, edge states are also related to the presence of zig-zag edge atoms,  although they presented remarkable size effects. Physical properties of chiral  graphene nanoribbons and general edges can have a stong dependence on chirality.  We have analysed the properties of edge states in twisted bilayaer ribbons,  explaining their energy dispersion and spatial localization. The different splittings  were found in edge bands due to the inhomogeneous interplay coupling. For stacked  zig-zag atoms the coupling was larger than corresponding edge states splitted apart,  but edge states stemming from regions with stacking, where the interlayer coupling  was smaller and gave rise to zero energy bands. We have also been found that in the  edge regions where top and bottom zig-zag terminations were stacked, inter-ribbon  tunneling between the dispersions less zero energy states created bonding and  antibonding combination with energies away from the energy of the Dirac point. The  obtained results were found in good agreement with previously obtained results.