Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911876456120320 |
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| author | Biswas, Sougata Chakrabarti, Arunava |
| author_facet | Biswas, Sougata Chakrabarti, Arunava |
| contents | We analyze the topological properties of a family of generalized Su-Schrieffer-Heeger (SSH) chains and mesh geometries. In both the geometries the usual staggering in the distribution of the two overlap integrals is delayed (in space) by the inclusion of a third (additional) hopping term. A tight-binding Hamiltonian is used to unravel the topological phases, characterized by a topological invariant. While in the linear chains, the topological invariant (the Zak phase) always appears to be quantized, in the quasi-one dimensional strip geometries and the generalized SSH mesh patterns the quantization of the Zak phase is sensitive to the strength of the additional interaction (the `extra' hopping integral). We study its influence thoroughly and explore the edge states and their robustness against disorder in the cross-linked generalized SSH mesh geometries. The systems considered here can be taken to model (though crudely) two-dimensional polymers where the cross-linking brings in non-trivial modification of the energy bands and transport properties. In addition to the topological features studied, we provide a prescription to unravel any flat, non-dispersive energy bands in the mesh geometries, along with the structure and distribution of the compact localized eigenstates. Our results are analytically exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes Biswas, Sougata Chakrabarti, Arunava Mesoscale and Nanoscale Physics We analyze the topological properties of a family of generalized Su-Schrieffer-Heeger (SSH) chains and mesh geometries. In both the geometries the usual staggering in the distribution of the two overlap integrals is delayed (in space) by the inclusion of a third (additional) hopping term. A tight-binding Hamiltonian is used to unravel the topological phases, characterized by a topological invariant. While in the linear chains, the topological invariant (the Zak phase) always appears to be quantized, in the quasi-one dimensional strip geometries and the generalized SSH mesh patterns the quantization of the Zak phase is sensitive to the strength of the additional interaction (the `extra' hopping integral). We study its influence thoroughly and explore the edge states and their robustness against disorder in the cross-linked generalized SSH mesh geometries. The systems considered here can be taken to model (though crudely) two-dimensional polymers where the cross-linking brings in non-trivial modification of the energy bands and transport properties. In addition to the topological features studied, we provide a prescription to unravel any flat, non-dispersive energy bands in the mesh geometries, along with the structure and distribution of the compact localized eigenstates. Our results are analytically exact. |
| title | Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2403.06556 |