PreprintCC BY 4.0arXiv
Reflectionless edge states in Dirac models of topological insulators
Abstract
We study an effective model of topological insulators joined along a bent interface. The Hamiltonian is a Dirac operator 𝒟 = D1σ1 + D2σ2 + κ(x) σ3 on L2(ℝ2,ℂ2), where κ(x) represents a domain wall with a corner: while initially straight, it undergoes a bend when passing from one side of ℝ2 to the other. For most energies in a spectral window centered at $0$, we construct a reflectionless edge state of 𝒟: a distorted plane wave with transmission coefficient of modulus $1$. This implies that 𝒟 admits modes confined near κ−1({0}), that travel through the bend with no loss neither to the bulk nor to reflection. Our result explains experimental observations from the physics literature, as well as our own numerical simulations.
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BibTeX
@misc{drouot2026reflectionless,
title = {{Reflectionless edge states in Dirac models of topological insulators}},
author = {Alexis Drouot},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16949},
eprint = {2609.16949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16949},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reflectionless edge states in Dirac models of topological insulators
AU - Alexis Drouot
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16949
UR - https://arxiv.org/abs/2609.16949
AB - We study an effective model of topological insulators joined along a bent interface. The Hamiltonian is a Dirac operator 𝒟 = D_1σ_1 + D_2σ_2 + κ(x) σ_3 on L^2(ℝ^2,ℂ^2), where κ(x) represents a domain wall with a corner: while initially straight, it undergoes a bend when passing from one side of ℝ^2 to the other. For most energies in a spectral window centered at $0$, we construct a reflectionless edge state of 𝒟: a distorted plane wave with transmission coefficient of modulus $1$. This implies that 𝒟 admits modes confined near κ^−1({0}), that travel through the bend with no loss neither to the bulk nor to reflection. Our result explains experimental observations from the physics literature, as well as our own numerical simulations.
ER -