Energetics and electronic structures of graphene corner edges
Graphene nanoribbons have been attracting so much attention in the filed of applied sciences due to their unusual electronic and magnetic properties those are intrinsically absent in bulk graphene, such as band-gap and magnetism. These properties strongly depend on atomic arrangements (armchair or zigzag edge orientation), ribbon widths, and ribbon lengths. Recently, experimental works demonstrated that zigzag edge graphene ribbons with 1200 corner is commonly formed in the graphene epitaxial growth on metal surfaces . This result is in sharp contrast to the dominant of armchair edges observed in theoretical calculations or experiments . In this work, we investigate energetics and electronic structures of zigzag graphene ribbons with 1200 corner (two zigzag edges), and 1500 corner (one zigzag edge, and one armchair edge) using first-principles total-energy calculations. We find that the formation energy of zigzag edges with 1200 corner is smaller than that of zigzag edge with 1500 corner, indicating the stability of the zigzag edges of graphene with 1200 corner observed in experimental results. We also find that both the 1200 and 1500 corner graphene ribbons are semiconductors in which band-gap decreases with increasing the length of zigzag edges. Around the 1200 edge corner of zigzag graphene ribbon, we find that the edge localized states are absent for the short zigzag region, while the edge state emerges along the zigzag edges of which length is larger than 1.3 nm. This unusual length dependence of the edge state is not found, however, in case of the 1500 edge corner of the graphene ribbon.
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