论文标题
散装通信
Bulk-and-edge to corner correspondence
论文作者
论文摘要
我们表明，二维带绝缘子具有消失的散装极化，遵守散装和边缘对应关系，表明散装的知识和两个相应的色带带结构唯一地决定了角度电荷的分数，而不论转角终止。此外，可以通过将晶体表示为具有极化的极化边缘区域的收集$ \ vec p^\ text {edge}_α$，其中integer $α$枚举边缘来获得与终止晶体的宏观电荷密度相关的物理可观察物。我们介绍了一种切割晶体，称为“ Wannier Cut”的特定方式，该晶体使我们能够计算$ \ vec p^\ text {edge}_α$。我们发现$ \ vec p^\ text {edge}_α$由两个部分组成：通过散装散装函数的二次张量表示的散装片段，以及与Wannier Edge偏振相对应的边缘件---通过削减Wannier Cut of Edge Subsystem的偏光。对于具有$ n $边缘的水晶，$ \ vec p^\ text {edge}_α$中的$ 2N $独立组件中，只有$ 2n-1 $独立于选择Wannier剪切，对应于物理可观察物：转角电荷和边缘dipoles。
We show that two-dimensional band insulators, with vanishing bulk polarization, obey bulk-and-edge to corner charge correspondence stating that the knowledge of the bulk and the two corresponding ribbon band structures uniquely determines the fractional part of the corner charge irrespective of the corner termination. Moreover, physical observables related to macroscopic charge density of a terminated crystal can be obtained by representing the crystal as collection of polarized edge regions with polarizations $\vec P^\text{edge}_α$, where the integer $α$ enumerates the edges. We introduce a particular manner of cutting a crystal, dubbed "Wannier cut", which allows us to compute $\vec P^\text{edge}_α$. We find that $\vec P^\text{edge}_α$ consists of two pieces: the bulk piece expressed via quadrupole tensor of the bulk Wannier functions' charge density, and the edge piece corresponding to the Wannier edge polarization---the polarization of the edge subsystem obtained by Wannier cut. For a crystal with $n$ edges, out of $2n$ independent components of $\vec P^\text{edge}_α$, only $2n-1$ are independent of the choice of Wannier cut and correspond to physical observables: corner charges and edge dipoles.
