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Finite-width effects for the localized edge modes in zigzag graphene nanoribbons

机译：之字形石墨烯纳米带中局部边缘模式的有限宽度效应

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摘要

A matrix formalism is used to derive the analytical Green's functions describing correlations between any two atomic sites on a zigzag (ZZ) graphene nanoribbon, incorporating modified electronic hopping values between edge sites that may be distinct from the hopping between interior sites. An analysis of the poles of our Green's functions shows two distinct types of localized edge modes in the electronic spectrum. The first of these, the "zero" mode, is a topologically induced mode arising from the bipartite honeycomb lattice structure of graphene and is always present along ZZ edges. The second type of localized edge mode is present at edges when the edge-to-bulk hopping ratio deviates significantly from unity. The correlations between edge sites are found to exhibit strikingly different features when mediated by the zero edge mode compared with mediation by the "modified" edge mode. In particular, the zero-mode spectral intensity for correlations between two atomic sites along opposite edges can be comparable in strength with that between two sites on the same edge of a finite-width ribbon, before it eventually tends to zero as the ribbon width tends to infinity. This remarkable behavior shows a strong dependence on the sublattice labels of the sites and is in contrast with properties of the modified hopping edge modes. The explicit form of our analytical expressions for the electronic spectrum enables us to predict the zero-mode properties (including frequency, spatial attenuation, and intensity) when the hopping values along ZZ edges are modified.
机译：矩阵形式主义用于导出描述锯齿形（ZZ）石墨烯纳米带上任意两个原子位点之间的相关性的分析格林函数，并结合了可能不同于内部位点之间跳变的边缘位点之间的修改后的电子跳变值。对我们格林函数极点的分析表明，电子光谱中存在两种不同类型的局部边缘模式。第一个是“零”模式，是由石墨烯的二元蜂窝状晶格结构引起的拓扑诱导模式，始终沿ZZ边缘出现。当边缘与本体的跳变比明显偏离单位时，第二种类型的局部边缘模式出现在边缘。发现与通过“修改的”边缘模式进行调解相比，当通过零边缘模式进行调解时，边缘位置之间的相关性表现出显着不同的特征。尤其是，沿宽度方向趋向于边缘的两个原子位点之间的相关性的零模光谱强度可以与有限宽度色带的相同边缘上的两个位点之间的强度相媲美，然后随着带宽度的趋向最终趋于零。到无穷远。这种显着的行为显示出对位点的亚晶格标记的强烈依赖性，并且与修改后的跳变边沿模式的特性形成对比。当我们修改沿ZZ边缘的跳变值时，我们对电子频谱的分析表达式的显式形式使我们能够预测零模属性（包括频率，空间衰减和强度）。

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  • 来源
    《Physical review》 |2016年第23期|235136.1-235136.12|共12页
  • 作者

    Arash Akbari-Sharbaf; Michael G. Cottam;

  • 作者单位

    Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada,Departement de Physique, Universite de Sher-brooke, Sherbrooke, Quebec, Canada J1K 2R1;

    Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada,Departement de Physique, Universite de Sher-brooke, Sherbrooke, Quebec, Canada J1K 2R1;

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