A rigorous proof of non-existence of edge state in the semi-infinite   armchair edged graphene
  With the help of transfer matrix method, the conditions for the existence of the edge states in the semi-infinite armchair edged graphene is given. We discuss zero-energy and non-zero-energy edge states separately, and show the nonexistence of the edge states in the model analytically and rigorously. 
Yuanyuan Zhao, Wei Li and Ruibao Tao
cond-mat.mes-hall