Edge states in rationally terminated honeycomb structures

Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of zigzag type and those of armchair type, generalizing the classical zigzag and armchair edges. We prove that zero-energy/flat-band edge states arise for edges of zigzag type, but never for those of armchair type. We exhibit explicit formulae for flat-band edge states when they exist. We produce strong evidence for the existence of dispersive (nonflat) edge state curves of nonzero energy for most l.

Automated summary

This article examines the tight binding model of graphene with sharp edges along a translational symmetry direction of the underlying lattice. The research classifies these edges into zigzag and armchair types, showing that zero-energy/flat-band edge states only occur in zigzag edges. The study provides explicit formulas for flat-band edge states and presents strong evidence of dispersive (nonflat) edge state curves of nonzero energy for most edges.