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Using first-principles calculations of graphene having high-symmetrydistortion or defects, we investigate band gap opening by chiral symmetrybreaking, or intervalley mixing, in graphene and show an intuitive picture ofunderstanding the gap opening in terms of local bonding and antibondinghybridizations. We identify that the gap opening by chiral symmetry breaking inhoneycomb lattices is an ideal two-dimensional (2D) extension of the Peierlsmetal-insulator transition in 1D linear lattices. We show that the spontaneousKekule distortion, a 2D version of the Peierls distortion, takes place inbiaxially strained graphene, leading to structural failure. We also show thatthe gap opening in graphene antidots and armchair nanoribbons, which has beenattributed usually to quantum confinement effects, can be understood with thechiral symmetry breaking.

Band gap opening by two-dimensional manifestation of Peierls instability in graphene