DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES

Charles Louis Fefferman (1) , Sonia Fliss (2, 3) , Michael Weinstein (4)

1 Department of Mathematics - Princeton University
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
3 UMA - Unité de Mathématiques Appliquées
4 Department of Applied Physics and Applied Mathematics [New York]

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 formulas for flat band edge states when they exist. We produce strong evidence for the existence of dispersive (non flat) edge state curves of nonzero energy for most l.

Mots clés: tight binding model; edge states; honeycomb structure; discrete operator on a graph

Domaines: Equations aux dérivées partielles [math.AP]

Charles Louis Fefferman, Sonia Fliss, Michael Weinstein. DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES. Communications on Pure and Applied Mathematics, inPress, ⟨10.1002/cpa.22141⟩. ⟨hal-03606004⟩