Completely flat bands and fully localized states on surfaces of anisotropic diamond-lattice models

Abstract

We discuss flat-band surface states on the (111) surface in the tight-binding model with nearest-neighbor hopping on the diamond lattice, in analogy to the flat-band edge states in graphene with a zigzag edge. The bulk band is gapless, and the gap closes along a loop in the Brillouin zone. The verge of the flat-band surface states is identical with this gap-closing loop projected onto the surface plane. When anisotropies in the hopping integrals increase, the bulk gap-closing points move and the distribution of the flat-band states expands in the Brillouin zone. Then when the anisotropy is sufficiently large, the surface flat bands cover the whole Brillouin zone. Because of the completely flat bands, we can construct surface-state wavefunctions which are localized in all the three directions.

9 pages, 9 figures

References in corpus (6)

• Electric Field Effect in Atomically Thin Carbon Films
• The Zak phase and the existence of edge states in graphene
• A new magnetic field dependence of Landau levels on a graphene like structure
• d+id' Chiral Superconductivity in Bilayer Silicene
• Stabilization mechanism of edge states in graphene
• Zero modes and the edge states of the honeycomb lattice

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