1304.7592 (Ryuji Takahashi et al.)

Completely flat band and fully localized states on boundaries of
anisotropic honeycomb/diamond-lattice models    [PDF]

Ryuji Takahashi, Shuichi Murakami

We discuss flat-band boundary states in the tight-binding model with nearest-neighbor hopping on the honeycomb and diamond lattices. As is similar to the flat-band edge states in graphene with a zigzag edge, flat-band surface states also appear in the tight-binding model on the diamond lattice. In the models on these bipartite lattices, the flat-band states are localized on the edge/surface and partially cover the Brillouin zone. When anisotropies in the hopping integrals increase, the bulk gapless points move and the distribution of the flat-band states expands in the Brillouin zone, and then when the anisotropy is sufficiently large, the boundary flat bands cover the whole Brillouin zone. Because of the completely flat bands at the boundary, one can construct wavefunctions which is localized in the direction along the boundary.

View original: http://arxiv.org/abs/1304.7592