论文标题
离散的蜂窝，理性边缘和边缘状态
Discrete honeycombs, rational edges and edge states
论文作者
论文摘要
考虑石墨烯的紧密绑定模型，沿边缘$ {\ bf l} $平行于基础晶格的转换对称性方向。我们将这种边缘$ {\ bf l} $分类为“曲折类型”和“扶手椅类型”的边缘，从而概括了经典的曲折和扶手椅边缘。我们证明，Zero/Flat Band边缘态为锯齿形类型的边缘出现，但从来没有扶手椅类型的边缘。当存在时，我们对平面边缘状态显示明确的公式。我们为大多数$ {\ bf l} $存在分散性（非平坦）边缘状态曲线的存在提供了有力的证据。
Consider the tight binding model of graphene, sharply terminated along an edge ${\bf l}$ parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges ${\bf l}$ 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 ${\bf l}$.
