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arXiv · 2306.15477

Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries

Jinbing Hu·Songlin Zhuang·Yi Yang
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Abstract

The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane ($\mathrm{RP}^2$) and the appearance of quadrupole insulating phase, which are enabled by momentum-space nonsymmorphic symmetries stemming from $\mathbb{Z}_2$ synthetic gauge fields. We show that the momentum-space nonsymmorphic symmetries quantize bulk polarization and Wannier-sector polarization nonlocally across different momenta, resulting in quantized corner charges and an isotropic binary bulk quadrupole phase diagram, where the phase transition is triggered by a bulk energy gap closing. Under open boundary conditions, the nontrivial bulk quadrupole phase manifests either trivial or nontrivial edge polarization, resulting from the violation of momentum-space nonsymmorphic symmetries under lattice termination. We present a concrete design for the $\mathrm{RP}^2$ quadrupole insulator based on acoustic resonator arrays and discuss its feasibility in optics, mechanics, and electrical circuits. Our results show that deforming the Brillouin manifold creates opportunities for realizing high-order band topology.

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Jinbing Hu, Songlin Zhuang, Yi Yang. 2023-06-27. Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries. https://doi.org/10.1103/physrevlett.132.213801

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