  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.
