A mathematical study of periodic band inversion
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911664597630976 |
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| author | Guo, Tyler Zworski, Maciej |
| author_facet | Guo, Tyler Zworski, Maciej |
| contents | We give a mathematical analysis of the periodic band inversion phenomenon observed by Tan--Devakul for an electron in a two-dimensional periodic potential coupled to a circularly polarized photon cavity mode. In the strong-coupling limit, we derive an effective Bloch Hamiltonian and prove convergence of the low-lying bands. For a cosine potential, we explain the periodic closing and reopening of the first spectral gap, prove the existence and generic persistence of Dirac cones at the gap-closing points, and compute the Chern numbers associated to isolated band clusters. We also show that higher isolated band clusters cannot persist in the small-coupling regime. Finally, we resolve an apparent sign discrepancy between Berry curvature computations and Chern numbers by tracking the descent from the covering space to the Brillouin torus. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A mathematical study of periodic band inversion Guo, Tyler Zworski, Maciej Mathematical Physics Spectral Theory 35H10, 35Q40, 81Q12, 81Q20, 81S10 We give a mathematical analysis of the periodic band inversion phenomenon observed by Tan--Devakul for an electron in a two-dimensional periodic potential coupled to a circularly polarized photon cavity mode. In the strong-coupling limit, we derive an effective Bloch Hamiltonian and prove convergence of the low-lying bands. For a cosine potential, we explain the periodic closing and reopening of the first spectral gap, prove the existence and generic persistence of Dirac cones at the gap-closing points, and compute the Chern numbers associated to isolated band clusters. We also show that higher isolated band clusters cannot persist in the small-coupling regime. Finally, we resolve an apparent sign discrepancy between Berry curvature computations and Chern numbers by tracking the descent from the covering space to the Brillouin torus. |
| title | A mathematical study of periodic band inversion |
| topic | Mathematical Physics Spectral Theory 35H10, 35Q40, 81Q12, 81Q20, 81S10 |
| url | https://arxiv.org/abs/2605.08481 |