Single-particle edge state in a local-resonance-induced topological band gap
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915838429233152 |
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| author | Srikanth, Garigipati Sai Qian, Kai Frankel, Ian Theocharis, Georgios Boechler, Nicholas Chaunsali, Rajesh |
| author_facet | Srikanth, Garigipati Sai Qian, Kai Frankel, Ian Theocharis, Georgios Boechler, Nicholas Chaunsali, Rajesh |
| contents | Topological metamaterials promise unprecedented wave control. Here, we theoretically and numerically investigate a one-dimensional Su-Schrieffer-Heeger (SSH) inspired stiffness dimer modified with a local resonator, which imparts a frequency-dependent effective stiffness to the unit cell. We demonstrate a two-step mechanism to create a topological local-resonance-induced band gap (LRG): first, a conventional Bragg-type band gap (BrG) is made topologically non-trivial via band inversion at a Dirac point; second, by tuning a dimerization parameter, the character of this non-trivial BrG is switched to that of an LRG via an intermediate flat band state. This process preserves the non-trivial topology without requiring gap closure within the LRG. Crucially, we find that when the resulting topological edge state intersects a characteristic frequency of the LRG -- specifically, an attenuation singularity where the effective stiffness vanishes -- it achieves extreme localization of vibrational energy. This state is confined to a single particle at the boundary, resulting in an inverse participation ratio of exactly unity, the theoretical limit for localization in a discrete system. Further, we demonstrate that while random disorder scatters the frequency of this mode, introducing tuned boundaries stabilizes the single-particle mode over a broad parameter range. Our findings provide a clear pathway to designing ultra-localized, topologically protected states in low-frequency regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Single-particle edge state in a local-resonance-induced topological band gap Srikanth, Garigipati Sai Qian, Kai Frankel, Ian Theocharis, Georgios Boechler, Nicholas Chaunsali, Rajesh Applied Physics Topological metamaterials promise unprecedented wave control. Here, we theoretically and numerically investigate a one-dimensional Su-Schrieffer-Heeger (SSH) inspired stiffness dimer modified with a local resonator, which imparts a frequency-dependent effective stiffness to the unit cell. We demonstrate a two-step mechanism to create a topological local-resonance-induced band gap (LRG): first, a conventional Bragg-type band gap (BrG) is made topologically non-trivial via band inversion at a Dirac point; second, by tuning a dimerization parameter, the character of this non-trivial BrG is switched to that of an LRG via an intermediate flat band state. This process preserves the non-trivial topology without requiring gap closure within the LRG. Crucially, we find that when the resulting topological edge state intersects a characteristic frequency of the LRG -- specifically, an attenuation singularity where the effective stiffness vanishes -- it achieves extreme localization of vibrational energy. This state is confined to a single particle at the boundary, resulting in an inverse participation ratio of exactly unity, the theoretical limit for localization in a discrete system. Further, we demonstrate that while random disorder scatters the frequency of this mode, introducing tuned boundaries stabilizes the single-particle mode over a broad parameter range. Our findings provide a clear pathway to designing ultra-localized, topologically protected states in low-frequency regimes. |
| title | Single-particle edge state in a local-resonance-induced topological band gap |
| topic | Applied Physics |
| url | https://arxiv.org/abs/2603.05611 |