$\mathbb{Z}_2$ topological invariants from the Green's function diagonal zeros
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908694591045632 |
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| author | Simon, Florian Morice, Corentin |
| author_facet | Simon, Florian Morice, Corentin |
| contents | We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's function in the orbital basis provide a direct and visual way to calculate the strong and weak $\mathbb{Z}_2$ topological invariants. We introduce the surface of crossings of diagonal zeros in the Brillouin zone, and show that it separates time-reversal invariant momenta (TRIMs) of opposite parity in two-band models, enabling the visual computation of the $\mathbb{Z}_2$ invariants by counting the relevant TRIMs on either side. In three-band systems, a similar property holds in every case except when a trivial band is added in the band gap of a non-trivial two-band system, reminiscent of the band topology of fragile topological insulators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}_2$ topological invariants from the Green's function diagonal zeros Simon, Florian Morice, Corentin Mesoscale and Nanoscale Physics We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's function in the orbital basis provide a direct and visual way to calculate the strong and weak $\mathbb{Z}_2$ topological invariants. We introduce the surface of crossings of diagonal zeros in the Brillouin zone, and show that it separates time-reversal invariant momenta (TRIMs) of opposite parity in two-band models, enabling the visual computation of the $\mathbb{Z}_2$ invariants by counting the relevant TRIMs on either side. In three-band systems, a similar property holds in every case except when a trivial band is added in the band gap of a non-trivial two-band system, reminiscent of the band topology of fragile topological insulators. |
| title | $\mathbb{Z}_2$ topological invariants from the Green's function diagonal zeros |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2504.00800 |