Novel physical properties have been reported recently by stacking graphene-like systems in different configurations. Here, we explore the nature of emergent localized states at the edges of twisted bilayer graphene nanoribbons. Using an extended tight-binding Hamiltonian, which includes hopping energy within a wide atomic neighborhood, we investigate the electronic states responsible for the transport along the four graphene nanoribbon terminals. Our emphasis is on discussing how the electronic and transport responses of the terminals are influenced by the symmetries of the stacking region, the twisted angle between the crossed zigzag nanoribbons, and the width of the ribbons. Our findings show a direct connection between the number of nonequivalent sites on the edge of the stacking region and the localized states, which aligns with reported scanning tunneling spectroscopy measurements. We found that the twist angle is the most powerful tool for controlling the transport responses in these four-terminal devices, enabling special electronic beam splitter phenomena.
Vidarte et al. (Fri,) studied this question.