论文标题
零能状态位于四极拓扑绝缘子的任意边缘附近
Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
论文作者
论文摘要
平方晶格上的二维四极拓扑绝缘子是高阶拓扑绝缘子的典型例子。它在其$ 90^{\ circ} $拐角处的每个$ e $ corners内部的每个$ e $ the $ e $都设置为$ e $的$ 90^{\ circ} $ corner的每个边缘状态，为简单起见，$ e $等于零。尽管边缘状态的外观已在仅$ 90^{\ circ} $角的简单系统中显示出来，但不确定是否可以在复杂的边缘附近出现类似的本地化状态，该状态是否可以出现在$ e = 0 $附近，由多个$ 90^{\ circ} $和$ 270^{\ circ} $ Corners组成。在这里，我们提出了一种数值方法，以确定位于任意边缘附近的零能状态的波函数。此方法使我们能够证明，如果边缘由奇数角组成，则在$ e = 0 $中出现一个本地化状态。相比之下，如果边缘包括均匀数量的角，本地化状态的能量不可避免地会偏离$ e = 0 $。
A two-dimensional quadrupole topological insulator on a square lattice is a typical example of a higher-order topological insulator. It hosts an edge state localized near each of its $90^{\circ}$ corners at an energy $E$ inside the band gap, where $E$ is set equal to zero for simplicity. Although the appearance of an edge state has been shown in simple systems with only $90^{\circ}$ corners, it is uncertain whether a similar localized state can appear at $E = 0$ near a complicated edge consisting of multiple $90^{\circ}$ and $270^{\circ}$ corners. Here, we present a numerical method to determine the wavefunction of a zero-energy state localized near an arbitrary edge. This method enables us to show that one localized state appears at $E = 0$ if the edge consists of an odd number of corners. In contrast, the energy of localized states inevitably deviates from $E = 0$ if the edge includes an even number of corners.
