Real-projective-plane hybrid-order topological insulator realized in phononic crystals

2023/11/28 by Lai, Pengtao, Wu, Jien, Pu, Zhenhang +7 · 4 citations
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

paper · doi:10.48550/arxiv.2311.16756

Abstract

The manifold of the fundamental domain of the Brillouin zone is always considered to be a torus. However, under the synthetic gauge field, the Brillouin manifold can be modified by the projective symmetries, resulting in unprecedented topological properties. Here, we realize a real-projective-plane hybrid-order topological insulator in a phononic crystal by introducing the Z₂ gauge field. Such insulator hosts two momentum-space non-symmorphic reflection symmetries, which change the Brillouin manifold from a torus to a real projective plane. These symmetries can simultaneously lead to Klein-bottle and quadrupole topologies in different bulk gaps. The non-symmorphic reflection symmetries on Brillouin real projective plane, edge states of Klein-bottle insulator, and corner states of quadrupole insulator are observed. These results evidence the hybrid-order topology on Brillouin manifold beyond the torus, and enrich the topological physics.

Cited by

• Non-Hermitian Exceptional Topology on a Klein Bottle Photonic Circuit
• Topological non-Abelian gauge structures in Cayley-Schreier lattices
• Unconventional hybrid-order topological insulators
• Non-Hermitian topological electric circuits with projective symmetry

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