Edge states of zigzag graphene nanoribbons with B and N doping at edge atoms

Using a tight binding model, we theoretically study the electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons where the outermost C atoms of zigzag graphene nanoribbons are replaced with B and N atoms. We show that the flat bands and edge states appear at the Fermi level when the number of B and N atoms are equal except the case of six times supercell. To investigate the origin of the edge states in BCN nanoribbons, we consider the semi-infinite graphene sheet with zigzag edge where outermost C atoms are replaced with B and N atoms. We analytically demonstrate the presence of edge states at the zigzag edges and flat bands using a transfer matrix method.