Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916971130388480 |
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| author | Teo, Hau Tian Long, Yang Zou, Hong-yu Song, Kailin Xue, Haoran Ge, Yong Yuan, Shou-qi Sun, Hong-xiang Zhang, Baile |
| author_facet | Teo, Hau Tian Long, Yang Zou, Hong-yu Song, Kailin Xue, Haoran Ge, Yong Yuan, Shou-qi Sun, Hong-xiang Zhang, Baile |
| contents | Bulk-boundary correspondence is the foundational principle of topological physics, first established in the quantum Hall effect, where a $D$-dimensional topologically nontrivial bulk gives rise to $(D-1)$-dimensional boundary states. The advent of higher-order topology has generalized this principle to a hierarchical chain, enabling topological states to appear at $(D-2)$ or even lower-dimensional boundaries. To date, all known realizations of topological systems must require a topologically nontrivial bulk to initiate the chain of action for bulk-boundary correspondence. Here, in an acoustic crystal platform, we experimentally demonstrate an exception to this paradigm--embedded topology in a trivial bulk--where the bulk-boundary correspondence originates from a trivial bulk. Rather than relying on global symmetries, we employ projective crystal symmetry, which induces nontrivial topology not at the outset in the $D$-dimensional bulk, but midway through the correspondence hierarchy in lower-dimensional boundaries. We further realize a three-dimensional system exhibiting embedded topology that supports zero-dimensional topological states, achieving the longest possible chain of action for such an unconventional bulk-boundary correspondence in physical space. Our work experimentally establishes a new form of bulk-boundary correspondence initiated from a trivial bulk, opening additional degrees of freedom for the design of robust topological devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry Teo, Hau Tian Long, Yang Zou, Hong-yu Song, Kailin Xue, Haoran Ge, Yong Yuan, Shou-qi Sun, Hong-xiang Zhang, Baile Mesoscale and Nanoscale Physics Bulk-boundary correspondence is the foundational principle of topological physics, first established in the quantum Hall effect, where a $D$-dimensional topologically nontrivial bulk gives rise to $(D-1)$-dimensional boundary states. The advent of higher-order topology has generalized this principle to a hierarchical chain, enabling topological states to appear at $(D-2)$ or even lower-dimensional boundaries. To date, all known realizations of topological systems must require a topologically nontrivial bulk to initiate the chain of action for bulk-boundary correspondence. Here, in an acoustic crystal platform, we experimentally demonstrate an exception to this paradigm--embedded topology in a trivial bulk--where the bulk-boundary correspondence originates from a trivial bulk. Rather than relying on global symmetries, we employ projective crystal symmetry, which induces nontrivial topology not at the outset in the $D$-dimensional bulk, but midway through the correspondence hierarchy in lower-dimensional boundaries. We further realize a three-dimensional system exhibiting embedded topology that supports zero-dimensional topological states, achieving the longest possible chain of action for such an unconventional bulk-boundary correspondence in physical space. Our work experimentally establishes a new form of bulk-boundary correspondence initiated from a trivial bulk, opening additional degrees of freedom for the design of robust topological devices. |
| title | Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2508.03033 |