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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.03699 |
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| _version_ | 1866913598294458368 |
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| author | Lin, Ling Lee, Chaohong |
| author_facet | Lin, Ling Lee, Chaohong |
| contents | The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a {multipole winding number} (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number Lin, Ling Lee, Chaohong Mesoscale and Nanoscale Physics Quantum Gases The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a {multipole winding number} (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs. |
| title | Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number |
| topic | Mesoscale and Nanoscale Physics Quantum Gases |
| url | https://arxiv.org/abs/2401.03699 |