Peierls Instability in Hexagonal Lattices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915584736755712 |
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| author | Gontier, David Roussigné, Thaddeus Séré, Éric |
| author_facet | Gontier, David Roussigné, Thaddeus Séré, Éric |
| contents | We investigate a conventional tight-binding model for graphene, where distortion of the honeycomb lattice is allowed, but penalized by a quadratic energy. We prove that the optimal 3-periodic lattice configuration has Kekulé O-type symmetry, and that for a sufficiently small elasticity parameter, the minimizer is not translation-invariant. Conversely, we prove that for a large elasticity parameter the translation-invariant configuration is the unique minimizer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Peierls Instability in Hexagonal Lattices Gontier, David Roussigné, Thaddeus Séré, Éric Mathematical Physics Materials Science 35B38, 35Q40, 81V74 We investigate a conventional tight-binding model for graphene, where distortion of the honeycomb lattice is allowed, but penalized by a quadratic energy. We prove that the optimal 3-periodic lattice configuration has Kekulé O-type symmetry, and that for a sufficiently small elasticity parameter, the minimizer is not translation-invariant. Conversely, we prove that for a large elasticity parameter the translation-invariant configuration is the unique minimizer. |
| title | Peierls Instability in Hexagonal Lattices |
| topic | Mathematical Physics Materials Science 35B38, 35Q40, 81V74 |
| url | https://arxiv.org/abs/2510.24230 |