Mechanical Weyl Modes in Topological Maxwell Lattices

We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, charac...

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Bibliographic Details
Published in:Physical review letters 2016-04, Vol.116 (13), p.135503-135503, Article 135503
Main Authors: Rocklin, D Zeb, Chen, Bryan Gin-Ge, Falk, Martin, Vitelli, Vincenzo, Lubensky, T C
Format: Article
Language:English
Subjects:
Brillouin zone
Degrees of freedom
Fermions
Lattices
Mathematical analysis
Origins
Strategy
Topology
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Summary:We show that two-dimensional mechanical lattices can generically display topologically protected bulk zero-energy phonon modes at isolated points in the Brillouin zone, analogs of massless fermion modes of Weyl semimetals. We focus on deformed square lattices as the simplest Maxwell lattices, characterized by equal numbers of constraints and degrees of freedom, with this property. The Weyl points appear at the origin of the Brillouin zone along directions with vanishing sound speed and move away to the zone edge (or return to the origin) where they annihilate. Our results suggest a design strategy for topological metamaterials with bulk low-frequency acoustic modes and elastic instabilities at a particular, tunable finite wave vector.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.116.135503