Topological spectral bands with frieze groups

Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations...

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Bibliographic Details
Published in:Journal of mathematical physics 2024-06, Vol.65 (6)
Main Authors: Lux, Fabian R., Stoiber, Tom, Wang, Shaoyun, Huang, Guoliang, Prodan, Emil
Format: Article
Language:English
Subjects:
Algebra
Band spectra
Banded structure
Group theory
Resonators
Spectral bands
Subgroups
Topology
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Summary:Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations of the internal structures of the seed resonators, the dynamical matrices of the materials generate the full self-adjoint sector of the stabilized group C*-algebra of the frieze group. As a consequence, in applications where the positions, orientations and internal structures of the seed resonators are adiabatically modified, the spectral bands of the dynamical matrices carry a complete set of topological invariants that are fully accounted by the K-theory of the mentioned algebra. By resolving the generators of the K-theory, we produce the model dynamical matrices that carry the elementary topological charges, which we implement with systems of plate resonators to showcase several applications in spectral engineering. The paper is written in an expository style.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0127973