Discrete honeycombs, rational edges, and edge states

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Charles L. Fefferman, Sonia Fliss, Michael I. Weinstein
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引用次数: 0

Abstract

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.

离散蜂窝、有理边和边缘状态
考虑石墨烯的紧密结合模型,沿着与底层周期晶格的平移对称方向平行的边缘 l 进行尖锐终止。我们将这种边缘 l 划分为 "人字形 "和 "扶手椅形 "边缘,对经典的人字形和扶手椅形边缘进行了概括。我们证明,"之 "字型边缘会出现零能量/平带边缘状态,而 "扶手椅 "型边缘绝不会出现这种状态。我们展示了平带边缘态存在时的明确公式。我们提出了强有力的证据,证明对于大多数 l,存在非零能量的色散(非平坦)边缘状态曲线。
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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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