Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916590673461248 |
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| author | Crépel, Valentin Cano, Jennifer |
| author_facet | Crépel, Valentin Cano, Jennifer |
| contents | Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient prediction of superlattice and anomalous miniband topology from quantum geometry Crépel, Valentin Cano, Jennifer Mesoscale and Nanoscale Physics Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers. |
| title | Efficient prediction of superlattice and anomalous miniband topology from quantum geometry |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2406.17843 |