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arXiv 1604.07546cond-mat.mes-hall
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模型拓扑绝缘体设计的教学探讨

A pedagogic review on designing model topological insulators

Tanmoy Das

摘要:

遵循几个世纪以来的概念量子化的通量通过高斯曲率(欧拉特征)和它的连续分散到各种凝聚态的性质,如量子霍尔效应,拓扑不变量,我们可以建立一个简单的和相当普遍的理解各种现代拓扑绝缘体(TI)。形成一个周期性的晶格(这是一个非平凡的高斯曲率)的“回旋轨道”与施加磁场,或“手征轨道”与虚构的“动量空间磁场”(贝里曲率)保证其通量量子化,因此整数量子霍尔(IQH),量子自旋霍尔(QSH)绝缘体,分别发生。与所有类型的TI相关联的体边界对应关系规定,在边界处的某种“量”的泵浦或偏振必须与体中的通量量子化或拓扑不变量相关联。与IQH和QSH状态边缘的电荷或自旋极化不同,时间反转(TR)不变的Z2 TI将称为“TR极化”的数学量泵送到表面。这要求价电子的波函数(比如说,π_{ \uparrow }(k))在布里渊区的一半中切换到它的TR共轭(π_{ \downarrow }^*(-k))奇数次。这两个普遍的特征可以被认为是设计和预测各种TI的“目标”。例如,我们证明,当两个相邻的原子链或层组装有相反的自旋轨道耦合(SOC),作为TR合作伙伴到对方,系统自然成为一个Z2 TI。这篇评论提供了一个全面的概述各种概念,计算方案,和工程原理的TI。

英文摘要:

Following the centuries old concept of the quantization of flux through a Gaussian curvature (Euler characteristic) and its successive dispersal into various condensed matter properties such as quantum Hall effect, and topological invariants, we can establish a simple and fairly universal understanding of various modern topological insulators (TIs). Formation of a periodic lattice (which is a non-trivial Gaussian curvature) of 'cyclotron orbits' with applied magnetic field, or 'chiral orbits' with fictitious 'momentum space magnetic field' (Berry curvature) guarantees its flux quantization, and thus integer quantum Hall (IQH), and quantum spin-Hall (QSH) insulators, respectively, occur. The bulk-boundary correspondence associated with all classes of TIs dictates that some sort of pumping or polarization of a 'quantity' at the boundary must be associated with the flux quantization or topological invariant in the bulk. Unlike charge or spin polarizations at the edge for IQH and QSH states, the time-reversal (TR) invariant Z2 TIs pump a mathematical quantity called 'TR polarization' to the surface. This requires that the valence electron's wavefunction (say, ψ_{\uparrow} (k)) switches to its TR conjugate (ψ_{\downarrow}^* (-k)) odd number of times in half of the Brillouin zone. These two universal features can be considered as 'targets' to design and predict various TIs. For example, we demonstrate that when two adjacent atomic chains or layers are assembled with opposite spin-orbit coupling (SOC), serving as the TR partner to each other, the system naturally becomes a Z2 TI. This review delivers a holistic overview on various concepts, computational schemes, and engineering principles of TIs.

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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