Topological insulators and higher-order topological insulators from gauge-invariant one-dimensional lines
Topological insulators and higher-order topological insulators from gauge-invariant one-dimensional lines
复制标题
DOI：
10.1103/physrevb.102.085108
复制
发表时间：
2020-04
影响因子：
3.7
通讯作者：
Heqiu Li;K. Sun
中科院分区：
文献类型：
--
作者：
Heqiu Li;K. Sun
本文主要研究二维/三维拓扑绝缘体和高阶拓扑绝缘体的$Z_2$拓扑指数。我们表明，在存在的两重旋转对称或镜像对称，规范不变量可以定义为任意一维线的布里渊区。这些一维量为计算拓扑绝缘体的Z2指数提供了一条新的途径。与其中Z_2 $索引通常涉及具有全局定义的平滑量规的布里渊区中的2D平面的通用设置相比，该1D方法仅涉及布里渊区中的一些1D线而不需要全局量规。这种简化的方法可以用于任何具有双重晶体对称性的时间反演不变绝缘体，可以在32个点群中的30个中找到。此外，这个一维量可以进一步推广到高阶拓扑绝缘体来计算磁电极化率P_3。
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a two-fold-rotational symmetry or a mirror symmetry, a gauge-invariant quantity can be defined for arbitrary 1D lines in the Brillouin zone. Such 1D quantities provide a new pathway to compute the $Z_2$ index of topological insulators. In contrast to the generic setup, where the $Z_2$ index generally involves 2D planes in the Brillouin zone with a globally-defined smooth gauge, this 1D approach only involves some 1D lines in the Brillouin zone without requiring a global gauge. Such a simplified approach can be used in any time-reversal invariant insulators with a two-fold crystalline symmetry, which can be found in 30 of the 32 point groups. In addition, this 1D quantity can be further generalized to higher-order topological insulators to compute the magnetoelectric polarization $P_3$.