We investigated the energetics and electronic structure of B N -doped graphene employing density functional theory calculations with the generalized gradient approximation. Our calculations reveal that all of the B N -doped graphene structures are semiconducting, irrespective of the periodicity of the B N embedded into the graphene network. This is in contrast to graphene nanomeshes, which are either semiconductors or metals depending on the mesh arrangement. In B N -doped graphene, the effective masses for both electrons and holes are small. The band gap in the B N -doped graphene networks and the total energy of the B N -doped graphene are inversely proportional to the B N spacing. Furthermore, both properties depend on whether or not the graphene region possesses a Clar structure. In particular, the sheets with a Clar structure exhibit a wider band gap and a slightly lower total energy than those without a Clar structure.

We studied the energetics of two-dimensional heterostructures consisting of h-BN and graphene with respect to the border structure and heterobond species using the density functional theory. A BC heterobond is energetically preferable at the border between h-BN and graphene. We also found the polarization at the zigzag border increase the total energy of the heterostructures. Competition between the bond formation energy and the polarization energy leads to the chiral borders where BC heterobonds are dominant. By taking the formation process of the heterostructures into account, the zigzag border with BC heterobond is preferentially synthesized from graphene edges and under the hydrogen rich condition. A layered structure comprising a hexagonal covalent network endows graphene with unusual electronic structure which is characterized by pairs of linear dispersion bands at the Fermi level and six corners of the Brillouin zone causing unusual physical properties under appropriate conditions. 1-6) The electronic structure of graphene derivatives are sensitive to their dimensionality, size, and shapes, which are determined by the boundary condition imposed on the hexagonal network. Tubular forms of graphene (CNTs) are either metals or semiconductors, depending on their atomic arrangement along their circumference. 7-9) By imposing an open boundary condition, graphene nanoribbons exhibit similar variations in their electronic structure to the CNTs. The graphene nanoribbons with armchair or near armchair edges possess metallic and semiconducting electronic structures depending on their width and edge shape. The band gap of the nanoribbons with armchair and near armchair edges is inversely proportional to the ribbon width. 10-13) In contrast, the graphene nanoribbons with zigzag and near zigzag *

We study the energetics and electronic structures of MoS 2 nanoribbons with clean armchair, chiral, and zigzag edges by conducting the first-principle total energy calculations based on the density functional theory. Our calculations showed that the nanoribbon with zigzag edges is the most stable among the ribbons studied here. The ribbons with armchair or near armchair edges are semiconductors with direct band gap at the Γ point, owing to the large edge relaxation reducing unsaturated nature of edge atoms, while the ribbons with zigzag and near zigzag edges are metals with the finite density of state at the Fermi level. According to the asymmetric atomic arrangement in ribbons with the chiral and zigzag edges, they have polarity normal to the ribbon, which monotonically increase with increasing the edge angle.

We studied the energetics of two-dimensional in-plane heterostructures consisting of transition metal dichalcogenides, MoS2 and WS2, with respect to the border structure using density functional theory. A WS bond is energetically preferable at the border between MoS2 and WS2, so that the border tend to form WS bond as much as possible. We also found that the polarization at the zigzag border increases the total energy of the heterostructures. Competition between the bond formation energy and the polarization energy leads to chiral borders at which WS heterobonds are dominant. The border possesses type II band edge alignment with the band offsets of 0.16 and 0.28 eV for valence and conduction band edges, respectively.