We investigate the Dirac cone in α-graphdiyne, which is a predicted flat one-atom-thick allotrope of carbon using first-principles calculations. α-graphdiyne is derived from graphene where two acetylenic linkages (-C ≡C-) are inserted into the single bonds (-C-C-). Thus, α-graphdiyne possesses a larger lattice constant which subsequently affects its electronic properties. Band structures show that α-graphdiyne exhibits similar Dirac points and cone to graphene. Further, the tight-binding method is used to exploit the linear dispersion in the vicinity of Dirac points. Thanks to the larger lattice constant, α-graphdiyne yields a lower Fermi velocity, which might make itself an ideal material to serve the anomalous integer quantum Hall effect.

Spin-polarized density functional theory has been used to study the properties of seven kinds of divacancies in graphitic boron nitride sheets. We find that some divacancies are magnetic and the symmetry of the sheets is broken by the distortion of atoms which are close to the vacancies. According to the formation energies, the neighboring boron and nitrogen vacancy pair is the most likely to form. Our calculations demonstrate that the divacancies can induce fundamental changes in the electronic properties of the sheet, making semiconducting–to–half-metallic transitions occur. The results can be used to customize the spintronics devices.

α-graphdiyne is a novel predicted Dirac cone material, which is similar to graphene. But the absence of a band gap significantly limits its practical applications. In order to extend this limitation, an opening of energy gap is needed. To this end, we resort to the nanoribbon structure of α-graphdiyne. This is a conventional proposal to open up the energy gaps in nanomaterials. The results show that both the armchair and the zigzag α-graphdiyne nanoribbons do generate energy gaps, which are width-dependent. In addition, the underlying mechanism of this opening is explored. The former is ascribed to the combination of quantum confinement and edges' effect, while the latter arises from the edge magnetic ordering. These novel nanoribbons with opening energy gaps would be potentially used in electronic devices.

A novel crystalline structure of hybrid monolayer hexagonal boron nitride (BN) and graphene is predicted by means of the first-principles calculations. This material can be derived via boron or nitrogen atoms which are substituted by carbon atoms evenly in the graphitic BN with vacancies. The corresponding structure is constructed from a BN hexagonal ring linking an additional carbon atom. The unit cell is composed of seven atoms, three of which are boron atoms, three are nitrogen atoms, and one is a carbon atom. It shows a similar space structure as graphene, which is thus coined as g-B3N3C. Two stable topological types associated with the carbon bond formation, i.e., C-N or C-B bonds, are identified. Interestingly, distinct ground states of each type, depending on C-N or C-B bonds, and electronic bandgap as well as magnetic properties within this material have been studied systematically. Our work demonstrates a practical and efficient access to electronic properties of two-dimensional nanostructures, providing an approach to tackling open fundamental questions in bandgap-engineered devices and spintronics.