ORIGINAL RESEARCH article
Front. Acoust.
Sec. Acoustic Metamaterials
Volume 3 - 2025 | doi: 10.3389/facou.2025.1615210
This article is part of the Research TopicAcoustic Topological Insulators: Envisioned Applications and Technology IntegrationView all 4 articles
The Acoustic Dirac Equation as a Model of Topological Insulators
Provisionally accepted
- University of Arizona, Tucson, United States
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The dynamical equations of motion of a discrete one-dimensional harmonic chain with side restoring forces is analogous to the relativistic Klein-Gordon equation. Dirac factorization of that discrete Klein-Gordon equation introduces two equations with time reversal (T) and parity (P) symmetry breaking conditions. The Dirac-factored equations enable the exploration of the properties of the solutions of the dynamical equations under PT symmetry breaking conditions. The spinor solutions of the Dirac factored equations describe two types of acoustic waves, one with a conventional topology (Berry phase equal to 0) and the other one with a non-conventional topology (Berry phase of π). In this latter case the acoustic wave is isomorphic to the quantum spin of an electron, also known as an acoustic pseudospin, which requires a closed path corresponding to two Brillouin zones to recover the original spinor. We also investigate the topology of evanescent waves supported by the Dirac factored equations. The interface between topologically conventional and non-conventional chains exhibits topological surface states. The Dirac-factored equations of motions of the one-dimensional harmonic chain with side springs can serve as a model for the investigation of the properties of acoustic topological insulators.
Keywords: topologial insulator, berry phase, Dirac equation, Klein - Gordon equation, Interface mode
Received: 20 Apr 2025; Accepted: 29 Aug 2025.
Copyright: © 2025 Basu, Runge and Deymier. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Abhirup Basu, University of Arizona, Tucson, United States
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