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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2304.11933 |
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| _version_ | 1866913210520567808 |
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| author | Liu, Feng |
| author_facet | Liu, Feng |
| contents | The Su-Schrieffer-Heeger (SSH) model is fundamental in topological insulators and relevant to understanding higher-order topological phases. This study explores the relationship between the $n$-dimensional SSH model and its $(n-1)$-dimensional counterpart, identifying a hierarchical structure in the Hamiltonian that allows us to solve an arbitrary $n$-dimensional SSH model analytically. By generalizing the bulk-edge correspondence principle to arbitrary dimensions in a higher-order fashion using the vectored Zak phase, we reveal a type of topological insulator called hierarchical topological insulators. In this hierarchical topological insulator, there exist intermediate-order topological interfacial states that are protected by subsymmetries and energy bands topology in a partial Brillouin zone. Furthermore, we compare the $n$-dimensional SSH model with the Benalcazar-Bernevig-Hughes (BBH) model, another essential model in higher-order topological phases similar to the two-dimensional SSH model with an extra flux of $π$ in each plaque. We find that the BBH model is another example of hierarchical topological insulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11933 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analytic Solution of $n$-dimensional Su-Schrieffer-Heeger Model Liu, Feng Superconductivity The Su-Schrieffer-Heeger (SSH) model is fundamental in topological insulators and relevant to understanding higher-order topological phases. This study explores the relationship between the $n$-dimensional SSH model and its $(n-1)$-dimensional counterpart, identifying a hierarchical structure in the Hamiltonian that allows us to solve an arbitrary $n$-dimensional SSH model analytically. By generalizing the bulk-edge correspondence principle to arbitrary dimensions in a higher-order fashion using the vectored Zak phase, we reveal a type of topological insulator called hierarchical topological insulators. In this hierarchical topological insulator, there exist intermediate-order topological interfacial states that are protected by subsymmetries and energy bands topology in a partial Brillouin zone. Furthermore, we compare the $n$-dimensional SSH model with the Benalcazar-Bernevig-Hughes (BBH) model, another essential model in higher-order topological phases similar to the two-dimensional SSH model with an extra flux of $π$ in each plaque. We find that the BBH model is another example of hierarchical topological insulators. |
| title | Analytic Solution of $n$-dimensional Su-Schrieffer-Heeger Model |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2304.11933 |