Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene
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arXiv
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| Natura: | Preprint |
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2026
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| author | Hitomi, Masaru Kawakami, Takuto Koshino, Mikito |
| author_facet | Hitomi, Masaru Kawakami, Takuto Koshino, Mikito |
| contents | We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical interpretation by directly relating the Landau levels to the quasi-band structure, allowing them to be understood as quantized orbits of quasi-band pockets. By using this method, we reveal distinctive spectral features, including nearly flat bands with weak magnetic-field dependence and highly degenerate levels arising from twelve off-center pockets. The resulting Landau levels are classified by two quantum numbers: the Landau-level index and the angular momentum associated with the underlying quasicrystalline symmetry. We also compute the magneto-optical conductivity and show that optical transitions follow angular-momentum selection rules enforced by the 12-fold symmetry. Our approach provides a symmetry-based and computationally efficient framework for bulk quantum magneto-optics in quasicrystalline van der Waals systems, predicting spectroscopic signatures accessible in high-field infrared and THz experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18854 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene Hitomi, Masaru Kawakami, Takuto Koshino, Mikito Mesoscale and Nanoscale Physics We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical interpretation by directly relating the Landau levels to the quasi-band structure, allowing them to be understood as quantized orbits of quasi-band pockets. By using this method, we reveal distinctive spectral features, including nearly flat bands with weak magnetic-field dependence and highly degenerate levels arising from twelve off-center pockets. The resulting Landau levels are classified by two quantum numbers: the Landau-level index and the angular momentum associated with the underlying quasicrystalline symmetry. We also compute the magneto-optical conductivity and show that optical transitions follow angular-momentum selection rules enforced by the 12-fold symmetry. Our approach provides a symmetry-based and computationally efficient framework for bulk quantum magneto-optics in quasicrystalline van der Waals systems, predicting spectroscopic signatures accessible in high-field infrared and THz experiments. |
| title | Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2604.18854 |