Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929487015313408 |
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| author | Baù, Nicolas Marrazzo, Antimo |
| author_facet | Baù, Nicolas Marrazzo, Antimo |
| contents | The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts in reciprocal space, hence implicitly assuming periodicity and homogeneity. Here, we introduce two space-resolved $\mathbb{Z}_{2}$ topological markers that are able to probe the local topology of the ground-state electronic structure also in the case of inhomogeneous and finite systems. The first approach leads to a generalized local spin-Chern marker, that usually remains well-defined also when the perpendicular component of the spin, $S_{z}$, is not conserved. The second marker is solely based on time-reversal symmetry, hence being more general. We validate our markers on the Kane-Mele model both in periodic and open boundary conditions, also in presence of disorder and including topological/trivial heterojunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems Baù, Nicolas Marrazzo, Antimo Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Materials Science The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts in reciprocal space, hence implicitly assuming periodicity and homogeneity. Here, we introduce two space-resolved $\mathbb{Z}_{2}$ topological markers that are able to probe the local topology of the ground-state electronic structure also in the case of inhomogeneous and finite systems. The first approach leads to a generalized local spin-Chern marker, that usually remains well-defined also when the perpendicular component of the spin, $S_{z}$, is not conserved. The second marker is solely based on time-reversal symmetry, hence being more general. We validate our markers on the Kane-Mele model both in periodic and open boundary conditions, also in presence of disorder and including topological/trivial heterojunctions. |
| title | Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Materials Science |
| url | https://arxiv.org/abs/2404.04598 |