论文标题
拓扑绝缘子和高阶拓扑绝缘子来自量规不变的1D线
Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
论文作者
论文摘要
在本手稿中，我们研究了对称性和拓扑之间的相互作用，重点是2D/3D拓扑绝缘子和高级拓扑绝缘器的$ Z_2 $拓扑指数。我们表明，在存在两倍的旋转对称性或镜像对称性的情况下，可以在布里渊区的任意1D线定义量规数量。这样的1D数量提供了一种新的途径来计算拓扑绝缘子的$ Z_2 $索引。与通用设置相反，$ Z_2 $索引通常涉及布里远区域的2D飞机，并具有全球定义的平滑量表，这种1D方法仅涉及Brillouin区域中的某些1D线，而无需全球仪表。这种简化的方法可以在具有两个倍晶体对称性的任何时间反转的绝缘子中使用，可以在32分组中的30个中找到。此外，该一维数量可以进一步推广到高阶拓扑绝缘子，以计算磁电化极化$ 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 $P_3$.
