Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry
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 superl...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.15.011004 |
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| _version_ | 1841543278620573696 |
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| author | Valentin Crépel Jennifer Cano |
| author_facet | Valentin Crépel Jennifer Cano |
| author_sort | Valentin Crépel |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-0b8d0fd2cc084179b58615b1940b9ecf |
| institution | Kabale University |
| issn | 2160-3308 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-0b8d0fd2cc084179b58615b1940b9ecf2025-01-13T15:02:36ZengAmerican Physical SocietyPhysical Review X2160-33082025-01-0115101100410.1103/PhysRevX.15.011004Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum GeometryValentin CrépelJennifer CanoTwo-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.http://doi.org/10.1103/PhysRevX.15.011004 |
| spellingShingle | Valentin Crépel Jennifer Cano Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry Physical Review X |
| title | Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry |
| title_full | Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry |
| title_fullStr | Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry |
| title_full_unstemmed | Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry |
| title_short | Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry |
| title_sort | efficient prediction of superlattice and anomalous miniband topology from quantum geometry |
| url | http://doi.org/10.1103/PhysRevX.15.011004 |
| work_keys_str_mv | AT valentincrepel efficientpredictionofsuperlatticeandanomalousminibandtopologyfromquantumgeometry AT jennifercano efficientpredictionofsuperlatticeandanomalousminibandtopologyfromquantumgeometry |