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Topological Boundary States and the Edge Chain in Semi-Infinite Two-Dimensional Insulators
Abstract
We show that it is possible to compute the adiabatically protected edge and corner states of semi-infinite, two-dimensional, topological insulators by considering the first layer of lattice sites, what we call the "edge chain," independently from the bulk. We start by accepting this claim as an ansatz, then, using the Shemesh theorem, we show that the edge states one finds using our procedure are adiabatically protected, provided we restrict ourselves to adiabatic evolutions that do not break chiral symmetry. We show explicit examples of our method in a 2D extension of the SSH model, the SSH3 model, the Haldane model and the Breathing Kagome Lattice.
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BibTeX
@misc{iakoub2026topological,
title = {{Topological Boundary States and the Edge Chain in Semi-Infinite Two-Dimensional Insulators}},
author = {Ilya Iakoub and Nicolas Levasseur and Richard MacKenzie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03173},
eprint = {2609.03173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03173},
}
RIS
TY - UNPB
TI - Topological Boundary States and the Edge Chain in Semi-Infinite Two-Dimensional Insulators
AU - Ilya Iakoub
AU - Nicolas Levasseur
AU - Richard MacKenzie
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03173
UR - https://arxiv.org/abs/2609.03173
AB - We show that it is possible to compute the adiabatically protected edge and corner states of semi-infinite, two-dimensional, topological insulators by considering the first layer of lattice sites, what we call the "edge chain," independently from the bulk. We start by accepting this claim as an ansatz, then, using the Shemesh theorem, we show that the edge states one finds using our procedure are adiabatically protected, provided we restrict ourselves to adiabatic evolutions that do not break chiral symmetry. We show explicit examples of our method in a 2D extension of the SSH model, the SSH3 model, the Haldane model and the Breathing Kagome Lattice.
ER -