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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 81V99
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Milestones
Received: 26 February 2020
Accepted: 16 January 2021
Published: 6 April 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Jonathan Michala | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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| Alexander Pierson | |
| Department of Mathematics Oregon State University Corvallis, OR United States |
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| Terry A. Loring | |
| Department of Mathematics and
Statistics University of New Mexico Albuquerque, NM United States |
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| Alexander B. Watson | |
| School of Mathematics University of Minnesota Twin Cities Minneapolis, MN United States |
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