Wave-packet propagation in a finite topological insulator and the spectral localizer index

Abstract

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.

arXiv comment29 pages, 16 figures

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