Experimental characterization of fragile topology in an acoustic metamaterial

Abstract

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.

arXiv comment4 pages, 3 figures + supplementary information (21 pages, 13 figures, 7 tables). Note the accompanying paper by Zhi-Da Song et al. "Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology"' posted on the same day on the arXiv

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• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Topological Materials Discovery from Crystal Symmetry
• Observation of non-Abelian topological semimetals and their phase transitions
• Geometric approach to fragile topology beyond symmetry indicators
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• Band Representations and Topological Quantum Chemistry
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles
• Topological correspondence between magnetic space group representations
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• Subdimensional topologies, indicators and higher order phases
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• From triple-point materials to multiband nodal links
• Corner modes of the breathing kagome lattice: origin and robustness
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Fragile topology in line-graph lattices with two, three, or four gapped flat bands
• General construction of flat bands with and without band crossings based on wave function singularity
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Intrinsic Superflat Bands in General Twisted Bilayer Systems
• Local markers for crystalline topology
• Tunable Fragile Topology in Floquet Systems
• Topological materials for full-vector elastic waves
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• Flat bands with band crossings enforced by symmetry representation
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• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
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• Pumping with Symmetry
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• Predicting the Characteristics of Defect Transitions on Curved Surfaces
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