论文标题
具有边界条件的一般连续体模型的形式主义，从非平地到琐碎拓扑类别的结合状态的传播以及在Weyl半学节点附近的一般表面状态结构
Formalism of general continuum models with boundary conditions, propagation of bound states from nontrivial to trivial topological classes, and the general surface-state structure near one node of a Weyl semimetal
论文作者
论文摘要
我们介绍具有边界条件的一般连续体模型的{\ em（对称性）形式主义}，并将其应用于具有最小的具有明确边界所需的自由度数量的模型：具有两组分的波浪函数和线性 - 内元素的模型。我们在1D（绝缘体），2D（量子异常的霍尔绝缘子）和3D（Weyl节点）中得出了哈密顿量和边界条件的最通用形式（A类），并通过分析计算并探索相应的通用/边缘/表面结构。在1D中，一个绑定状态存在于$ \ text {u}（1）$参数空间的一半中。考虑几个维度同时将模型联系在一起，并发现它们之间的重要关系。我们制定了一个完全表征Weyl点附近的散装对应的版本：沿着封闭投影的Weyl点的路径的表面状态光谱的手性等于Weyl点的Chern数。我们通过手性对称性（AIII类）得出模型的最通用形式，证明了如何自然地纳入形式主义。 We show that the (perhaps unexpected) existence of persistent bound states in the topologically trivial 1D class-A model is not accidental and has at least two topological explanations, by relating it to the topologically nontrivial 2D class-A (by viewing it as an effective 2D quantum anomalous Hall system) and 1D class-AIII (via deviation from the cases of chiral symmetry in the parameter space) models.我们将其识别为系统的“传播效应”，从而从拓扑非平凡的类别中结合了状态，在该阶段中，它们得到了保护和保证存在，并在维度或对称性上传播了相关的“邻近”，拓扑是微不足道的类别。
We present the {\em (symmetry-incorporating) formalism of general continuum models with boundary conditions} and apply it to the model with the minimal number of degrees of freedom necessary to have a well-defined boundary: a model with a two-component wave function and a linear-in-momentum Hamiltonian. We derive the most general forms (class A) of both the Hamiltonian and boundary condition in 1D (insulator), 2D (quantum anomalous Hall insulator), and 3D (Weyl node) and analytically calculate and explore the corresponding general bound/edge/surface-state structures. In 1D, one bound state exists in the half of the $\text{U}(1)$ parameter space of possible boundary conditions. Considering several dimensions simultaneously ties the models together and uncovers important relations between them. We formulate a version of bulk-boundary correspondence that fully characterizes the vicinity of a Weyl point: the chirality of the surface-state spectrum along a path enclosing the projected Weyl point is equal to the Chern number of the Weyl point. We demonstrate how symmetries are naturally incorporated into the formalism, by deriving the most general form of the model with chiral symmetry (class AIII). We show that the (perhaps unexpected) existence of persistent bound states in the topologically trivial 1D class-A model is not accidental and has at least two topological explanations, by relating it to the topologically nontrivial 2D class-A (by viewing it as an effective 2D quantum anomalous Hall system) and 1D class-AIII (via deviation from the cases of chiral symmetry in the parameter space) models. We identify this as a systematic "propagation effect", whereby bound states from topologically nontrivial classes, where they are protected and guaranteed to exist, propagate to the related, "adjacent" in dimension or symmetry, topologically trivial classes.
