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

TL;DR

This paper investigates flat-band surface states on the (111) surface of an anisotropic diamond-lattice model, revealing conditions for fully localized states and their relation to bulk gap-closing points.

Contribution

It demonstrates how anisotropy in hopping integrals leads to fully flat surface bands covering the entire Brillouin zone in a diamond lattice model.

Findings

Flat-band surface states exist on the (111) surface of the diamond lattice.

Increasing anisotropy causes the flat bands to expand in the Brillouin zone.

Sufficient anisotropy results in completely flat bands covering the whole zone.

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.