标题： 截断的$\mathbb{Z}_2$绝缘体的边缘谱 显示英文标题

标题： Edge spectrum for truncated $\mathbb{Z}_2$-insulators

摘要： 二维费米时间反演不变绝缘体——Kitaev表中的AII类——有两种不同的拓扑相。 这些相由$\mathbb{Z}_2$-指标来表征：Fu-Kane-Mele指标。 我们证明，如果两个具有不同指标的此类绝缘体占据包含任意大的球体的区域，那么所得算子的谱将填满体带隙。 我们的论证遵循两位作者在早期工作中为量子霍尔系统开发的反证法。 其核心在于证明，在足够大的球体中，$\mathbb{Z}_2$-指标仅能从体信息计算得出。 这是通过一个独立感兴趣的结论实现的：$\mathbb{Z}_2$-指标的局部迹公式。 显示英文摘要

摘要： Fermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. These are characterized by a $\mathbb{Z}_2$-index: the Fu-Kane-Mele index. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in an earlier work by two of the authors for quantum Hall systems. It boils down to showing that the $\mathbb{Z}_2$-index can be computed only from bulk information in sufficiently large balls. This is achieved via a result of independent interest: a local trace formula for the $\mathbb{Z}_2$-index.