High-root topological edge-state bands
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913993804742656 |
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| author | Dias, R. G. Madail, L. Marques, A. M. |
| author_facet | Dias, R. G. Madail, L. Marques, A. M. |
| contents | This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A simplified topological characterization of HRTIs with generalized boundary conditions is carried out based on the existence of edge-state bands in the infinite HRTI and the restrictions imposed by the boundary conditions. Edge states in finite or semi-infinite 1D HRTIs are shown to be a subset of evanescent states of the infinite system and mapped onto impurity states of the uniform chain with effective energy-dependent edge potentials. The latter result allows the determination of the edge state levels without needing the diagonalization of real space or bulk Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-root topological edge-state bands Dias, R. G. Madail, L. Marques, A. M. Mesoscale and Nanoscale Physics Strongly Correlated Electrons This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A simplified topological characterization of HRTIs with generalized boundary conditions is carried out based on the existence of edge-state bands in the infinite HRTI and the restrictions imposed by the boundary conditions. Edge states in finite or semi-infinite 1D HRTIs are shown to be a subset of evanescent states of the infinite system and mapped onto impurity states of the uniform chain with effective energy-dependent edge potentials. The latter result allows the determination of the edge state levels without needing the diagonalization of real space or bulk Hamiltonians. |
| title | High-root topological edge-state bands |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.12066 |