Wave-packet propagation in a finite topological insulator and the spectral localizer index
Wave-packet propagation in a finite topological insulator and the spectral localizer index
复制标题
DOI：
10.2140/involve.2021.14.209
复制
发表时间：
2020-01
期刊：
影响因子：
--
通讯作者：
Jonathan Michala;A. Pierson;T. Loring;Alexander B. Watson
中科院分区：
文献类型：
--
作者：
Jonathan Michala;A. Pierson;T. Loring;Alexander B. Watson
我们考虑有限拓扑绝缘体中的电子模型。我们对存在缺陷和随机无序的情况下位于结构边缘附近的电子波包的传播进行了数值研究。我们将传播与\emph{光谱定位指数}的计算进行比较：空间局部拓扑指数。我们发现，即使存在严重缺陷，波包也会沿着不同光谱定位器指数区域之间的边界传播，损失最小，没有无序。在无序的情况下，波包仍然沿着不同定位器指数区域之间的边界传播，但在传播时会损失大量质量。我们还发现，在无序的情况下，\emph{定位器间隙}（定位器指数“强度”的度量）远离边界的距离通常比没有无序的情况要小。基于这个结果，我们推测，只要边界两侧的定位器间隙足够大，沿着不同光谱定位器指数区域之间的边界传播的波包就不会损失显着的质量。
We consider a model of electrons in a finite topological insulator. We numerically study the propagation of electronic wave-packets localized near edges of the structure in the presence of defects and random disorder. We compare the propagation with computations of the \emph{spectral localizer index}: a spatially local topological index. We find that without disorder, wave-packets propagate along boundaries between regions of differing spectral localizer index with minimal loss, even in the presence of strong defects. With disorder, wave-packets still propagate along boundaries between regions of differing localizer index, but lose significant mass as they propagate. We also find that with disorder, the \emph{localizer gap}, a measure of the localizer index "strength", is generally smaller away from the boundary than without disorder. Based on this result, we conjecture that wave-packets propagating along boundaries between regions of differing spectral localizer index do not lose significant mass whenever the localizer gap is sufficiently large on both sides of the boundary.