Non-singular and singular flat bands in tunable phononic metamaterials
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Date
2023-04-18
Authors
Karki, Pragalv
Paulose, Jayson
Journal Title
Journal ISSN
Volume Title
Publisher
APS
Abstract
Dispersionless flat bands can be classified into two types: (1) non-singular flat bands whose eigenmodes
are completely characterized by compact localized states, and (2) singular flat bands that have a discontinuity
in their Bloch eigenfunctions at a band touching point with an adjacent dispersive band, thereby requiring
additional extended states to span their eigenmode space. In this study, we design and numerically demonstrate
two-dimensional thin-plate phononic metamaterials in which tunable flat bands of both kinds can be achieved.
Non-singular flat bands are achieved by fine tuning the ratio of the global tension and the bending stiffness in
triangular and honeycomb lattices of plate resonators. A singular flat band arises in a kagome lattice due to the
underlying lattice geometry, which can be made degenerate with two additional flat bands by tuning the plate
tension. A discrete model of the continuum thin-plate system reveals the interplay of geometric and mechanical
factors in determining the existence of flat bands of both types. The singular nature of the kagome lattice flat
band is established via a metric called the Hilbert-Schmidt distance calculated between a pair of eigenstates
infinitesimally close to the quadratic band touching point.We also simulate a phononic manifestation of a robust
boundary mode arising from the singular flat band and protected by real-space topology in a finite system. Our
theoretical and computational study establishes a framework for exploring flat-band physics in a tunable classical
system, and for designing phononic metamaterials with potentially useful sound manipulation capabilities.
Description
13 pages
Keywords
Acoustic phonons, Edge status, Elasticity, Flat bands
Citation
Karki, P., & Paulose, Jayson (2023). Non-singular and singular flat bands in tunable phononic metamaterials. Physical Review Research, 5(2), 1—13. https://doi.org/10.1103/PhysRevResearch.5.023036