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 [1]. This result is in sharp contrast to the dominant of armchair edges observed in theoretical calculations or experiments [2]. 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.

[1] J. Tian et al., Nano Lett. 11 (2011) 3663-3668; X. Li et al., Science 319 (2008) 1229-1232; C. O. Girit et al., Science 323 (2009) 1705-1708; X. Jia et al., Science 323 (2009) 1701-1705.
[2] S. Okada, Phys. Rev. B 77 (2008) 041408 (R); G. M. Rutter et al., Phys. Rev. B 81 (2010) 245408.