Electronic structure of covalent networks of triangular graphene flakes embedded in hBN

Covalent networks of triangular graphene flakes ([n]triangulenes) embedded in hexagonal boron nitride (hBN) were theoretically investigated using density functional theory. Our calculations reveal that the electronic structure of these in-plane heterostructures comprising B, C, and N atoms strongly depends on the arrangements of the constituent triangular graphene flakes and border atom species. Heterostructures comprising a copolymer of [n]triangulene and [m]triangulene embedded in hBN are tiny gap semiconductors or metals for which flat dispersion bands emerge near and at the Fermi level. A heterostructure comprising [3]triangulene is a semiconductor with a moderate direct gap of 0.7 eV, in which the band edges exhibit a flat band nature throughout the Brillouin zone. These flat band states are attributed to the hybridization between the non-bonding states of the triangulenes and the p(z) orbitals of the B and N atoms at the borders.