Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals

Abstract

Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond the conventional topological paradigms. Here, we discover experimentally that the nonsymmorphic $p4g$ acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, while the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexing topological phenomena and to reveal a topological transition triggered by the geometry-transition from the $p4g$ group to the $C_{4v}$ group which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates an instance that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions.

arXiv comment5 figures. Accepted by Nature Communications

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• Observation of a higher-order topological bound state in the continuum
• Higher-Order Weyl Semimetals
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• Higher-order topological superconductors from Weyl semimetals
• Second-order topological modes in two-dimensional continuous media
• Dirac cones and higher-order topology in quasi-continuous media
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• Simulating Floquet topological phases in static systems
• Floquet higher-order topological phases in momentum space
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• Topological Wannier cycles for the bulk and edges
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• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Unconventional hybrid-order topological insulators
• Topological reflection matrix
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