Using the density functional theory, we calculate electronic states of various nanoribbons and nanodiscs formed from selected two-dimensional materials, such as graphene, silicene, and hexagonal boron nitride. The main objective of the analysis is a search for zero-energy states in such systems, which is an important issue as their presence indicates certain topological properties associated with chirality. The analysis is also supported by calculating transport properties.
Keywords: 2D materials; density functional theory; finite-length nanoribbons; nanodiscs; zero-energy states; zigzag trigonal nanodiscs.