Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929682540134400 |
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| author | Hu, Jinbing Zhuang, Songlin Yang, Yi |
| author_facet | Hu, Jinbing Zhuang, Songlin Yang, Yi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15477 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries Hu, Jinbing Zhuang, Songlin Yang, Yi Mesoscale and Nanoscale Physics 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. |
| title | Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2306.15477 |