论文标题
有限拓扑绝缘子和光谱定位器指数中的波包传播
Wave-packet propagation in a finite topological insulator and the spectral localizer index
论文作者
论文摘要
我们考虑有限拓扑绝缘子中电子模型。我们从数值上研究了在存在缺陷和随机疾病的情况下，在结构边缘附近的电子波包的传播。我们将传播与\ emph {光谱定位器索引}的计算进行比较：一个空间局部拓扑索引。我们发现，如果没有障碍，波包也会沿着不同光谱定位器指数的区域之间的边界传播，即使在存在强缺陷的情况下，损失也很小。随着疾病的影响，波包仍然沿着不同定位器指数区域之间的边界传播，但在传播时会失去巨大的质量。我们还发现，对于\ emph {lotizer gap}的疾病，对定位器索引“强度”的度量通常比没有混乱的范围要小。基于此结果，我们猜测波动包沿不同光谱定位器指数区域之间边界传播的波包在边界两侧都足够大时都不会失去显着的质量。
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.
