Topological transition as a percolation of the Berry curvature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910919753203712 |
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| author | Kim, Han-Byul Yuk, Taewon Sin, Sang-Jin |
| author_facet | Kim, Han-Byul Yuk, Taewon Sin, Sang-Jin |
| contents | We first study the importance of the sign of the Berry curvature in the Euler characteristic of the two-dimensional topological material with two bands. Then we report an observation of a character of the topological transition as a percolation of the sign of the Berry curvature. The Berry curvature F has peaks at the Dirac points, enabling us to divide the Brillouin zone into two regions depending on the sign of the F: one with the same sign with a peak and the other with the opposite sign. We observed that when the Chern number is non-zero, the oppositely signed regions are localized. In contrast, in the case of a trivial topology, the oppositely signed regions are delocalized dominantly. Therefore, the oppositely signed region will percolate under the topological phase transition from non-trivial to trivial. We checked this for several models including the Haldane model, the extended Haldane model, and the QWZ model. Our observation may serve as a novel feature of the topological phase transition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_21098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological transition as a percolation of the Berry curvature Kim, Han-Byul Yuk, Taewon Sin, Sang-Jin Mesoscale and Nanoscale Physics We first study the importance of the sign of the Berry curvature in the Euler characteristic of the two-dimensional topological material with two bands. Then we report an observation of a character of the topological transition as a percolation of the sign of the Berry curvature. The Berry curvature F has peaks at the Dirac points, enabling us to divide the Brillouin zone into two regions depending on the sign of the F: one with the same sign with a peak and the other with the opposite sign. We observed that when the Chern number is non-zero, the oppositely signed regions are localized. In contrast, in the case of a trivial topology, the oppositely signed regions are delocalized dominantly. Therefore, the oppositely signed region will percolate under the topological phase transition from non-trivial to trivial. We checked this for several models including the Haldane model, the extended Haldane model, and the QWZ model. Our observation may serve as a novel feature of the topological phase transition. |
| title | Topological transition as a percolation of the Berry curvature |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2407.21098 |