EDGE STATE DYNAMICS ALONG CURVED INTERFACES

Guillaume Bal; Simon Becker; Alexis Drouot; Clotilde Fermanian Kammerer; Jianfeng Lu; Alexander B. Watson

doi:10.1137/22M1489708

EDGE STATE DYNAMICS ALONG CURVED INTERFACES

Guillaume Bal, Simon Becker, Alexis Drouot, Clotilde Fermanian Kammerer, Jianfeng Lu, Alexander B. Watson

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit formulas for straight edges, we construct a family of solutions that propagates, for long times, unidirectionally and dispersion-free along the curved edge. We illustrate our results through various numerical simulations.

Original language	English (US)
Pages (from-to)	4219-4254
Number of pages	36
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	5
DOIs	https://doi.org/10.1137/22M1489708
State	Published - 2023

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© 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Keywords

Dirac equation
edge states
quantum mechanics
topological insulators

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10.1137/22M1489708

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abstract = "We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit formulas for straight edges, we construct a family of solutions that propagates, for long times, unidirectionally and dispersion-free along the curved edge. We illustrate our results through various numerical simulations.",

keywords = "Dirac equation, edge states, quantum mechanics, topological insulators",

author = "Guillaume Bal and Simon Becker and Alexis Drouot and Kammerer, {Clotilde Fermanian} and Jianfeng Lu and Watson, {Alexander B.}",

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AU - Bal, Guillaume

AU - Becker, Simon

AU - Drouot, Alexis

AU - Kammerer, Clotilde Fermanian

AU - Lu, Jianfeng

AU - Watson, Alexander B.

PY - 2023

Y1 - 2023

N2 - We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit formulas for straight edges, we construct a family of solutions that propagates, for long times, unidirectionally and dispersion-free along the curved edge. We illustrate our results through various numerical simulations.

AB - We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit formulas for straight edges, we construct a family of solutions that propagates, for long times, unidirectionally and dispersion-free along the curved edge. We illustrate our results through various numerical simulations.

KW - Dirac equation

KW - edge states

KW - quantum mechanics

KW - topological insulators

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

EDGE STATE DYNAMICS ALONG CURVED INTERFACES

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