Band gap opening by two-dimensional manifestation of Peierls instability   in graphene
  Using first-principles calculations of graphene having high-symmetry distortion or defects, we investigate band gap opening by chiral symmetry breaking, or intervalley mixing, in graphene and show an intuitive picture of understanding the gap opening in terms of local bonding and antibonding hybridizations. We identify that the gap opening by chiral symmetry breaking in honeycomb lattices is an ideal two-dimensional (2D) extension of the Peierls metal-insulator transition in 1D linear lattices. We show that the spontaneous Kekule distortion, a 2D version of the Peierls distortion, takes place in biaxially strained graphene, leading to structural failure. We also show that the gap opening in graphene antidots and armchair nanoribbons, which has been attributed usually to quantum confinement effects, can be understood with the chiral symmetry breaking. 
Sung-Hoon Lee, Hyun-Jong Chung, Jinseong Heo, Heejun Yang, Jaikwang   Shin, U-In Chung, and Sunae Seo
cond-mat.mtrl-sci