Vol. 14, No. 2, 2021

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

Jonathan Michala, Alexander Pierson, Terry A. Loring and Alexander B. Watson

Vol. 14 (2021), No. 2, 209–239
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 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 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.

Keywords
topological insulators, localizer index, wave-packet propagation, edge states, quantum mechanics, condensed matter physics, materials science
Mathematical Subject Classification 2010
Primary: 81V99
Milestones
Received: 26 February 2020
Accepted: 16 January 2021
Published: 6 April 2021

Communicated by Kenneth S. Berenhaut
Authors
Jonathan Michala
Department of Mathematics
University of Southern California
Los Angeles, CA
United States
Alexander Pierson
Department of Mathematics
Oregon State University
Corvallis, OR
United States
Terry A. Loring
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, NM
United States
Alexander B. Watson
School of Mathematics
University of Minnesota Twin Cities
Minneapolis, MN
United States