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arXiv · 2311.16756

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

Pengtao Lai·Jien Wu·Zhenhang Pu·Qiuyan Zhou·Jiuyang Lu·Hui Liu·Weiyin Deng·Hua Cheng·Shuqi Chen·Zhengyou Liu
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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 Z_2 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.

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Pengtao Lai, Jien Wu, Zhenhang Pu, Qiuyan Zhou, Jiuyang Lu, Hui Liu, Weiyin Deng, Hua Cheng, Shuqi Chen, Zhengyou Liu. 2023-11-28. Real-projective-plane hybrid-order topological insulator realized in phononic crystals. https://arxiv.org/abs/2311.16756

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