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arXiv 1008.0481cond-mat.mes-hall
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拓扑绝缘体边缘模的解析理论

Analytic Theory of Edge Modes in Topological Insulators

Shijun Mao, Yoshio Kuramoto, Ken-Ichiro Imura, Ai Yamakage

摘要:

对正方形晶格上的拓扑绝缘体紧束缚模型,解析地导出了无隙边缘模的谱和波函数。特别注意的是,在热力学极限的边缘几何形状,如直(1,0)和锯齿形(1,1)的边缘的依赖。其关键技术是识别结合在有效一维(1D)模型中的边缘状态与沿边缘的动量相湮灭的算子。在(1,0)边,边模存在于一维布里渊区的中心或边界附近,这取决于体激发能隙的位置。在(1,1)边中,边模总是存在于中心和边界附近。然而,取决于系统参数,该模式在布里渊区的中间不存在。在这种情况下,边界附近的边缘模式的结合能是非常小的,约为总能量标度的$10^{-3}$。讨论了这种微小能量标度的起源。

英文摘要:

Spectrum and wave function of gapless edge modes are derived analytically for a tight-binding model of topological insulators on square lattice. Particular attention is paid to dependence on edge geometries such as the straight (1,0) and zigzag (1,1) edges in the thermodynamic limit. The key technique is to identify operators that combine to annihilate the edge state in the effective one-dimensional (1D) model with momentum along the edge. In the (1,0) edge, the edge mode is present either around the center of 1D Brillouin zone or its boundary, depending on location of the bulk excitation gap. In the (1,1) edge, the edge mode is always present both at the center and near the boundary. Depending on system parameters, however, the mode is absent in the middle of the Brillouin zone. In this case the binding energy of the edge mode near the boundary is extremely small; about $10^{-3}$ of the overall energy scale. Origin of this minute energy scale is discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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