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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.12918 |
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| _version_ | 1866918413800046592 |
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| author | Jauslin, Ian Mastropietro, Vieri |
| author_facet | Jauslin, Ian Mastropietro, Vieri |
| contents | We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer Umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasi-periodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number-theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a Renormalization Group (RG) analysis of the imaginary-time, zero-temperature Green's functions, with number theoretic properties, and it is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out non-perturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability Jauslin, Ian Mastropietro, Vieri Strongly Correlated Electrons Mathematical Physics We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer Umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasi-periodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number-theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a Renormalization Group (RG) analysis of the imaginary-time, zero-temperature Green's functions, with number theoretic properties, and it is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out non-perturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected. |
| title | Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability |
| topic | Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2510.12918 |