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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.19332 |
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| _version_ | 1866910153410871296 |
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| author | Fontana, Pierpaolo Lepori, Luca Trombettoni, Andrea |
| author_facet | Fontana, Pierpaolo Lepori, Luca Trombettoni, Andrea |
| contents | The three-dimensional Hofstadter model exhibits a critical rational flux at which Weyl points emerge in the single-particle spectrum. We study the superconducting regime of the model in the presence of a Hubbard attractive interaction by tuning the magnetic flux across its critical value. We determine the phase diagram in the plane of the coprime pairs parametrizing the magnetic flux. We show that the system exhibits two distinct regimes separated by a critical flux $Φ_c$: for $Φ>Φ_c$, a semimetal-to-superconductor quantum phase transition occurs at a finite interaction strength ($U_c\neq0$), while for $Φ<Φ_c$ superconductivity arises for arbitrarily weak attraction, with a BCS-like exponential scaling of the gap due to the finiteness of the density of states. Close to the transition, we study the scaling behavior and identify the critical exponents. Our results highlight the interplay between magnetic band topology and attractive pairing in three-dimensional Hofstadter systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Superconducting properties of the three-dimensional Hofstadter-Hubbard model below the critical flux for Weyl points Fontana, Pierpaolo Lepori, Luca Trombettoni, Andrea Strongly Correlated Electrons Superconductivity The three-dimensional Hofstadter model exhibits a critical rational flux at which Weyl points emerge in the single-particle spectrum. We study the superconducting regime of the model in the presence of a Hubbard attractive interaction by tuning the magnetic flux across its critical value. We determine the phase diagram in the plane of the coprime pairs parametrizing the magnetic flux. We show that the system exhibits two distinct regimes separated by a critical flux $Φ_c$: for $Φ>Φ_c$, a semimetal-to-superconductor quantum phase transition occurs at a finite interaction strength ($U_c\neq0$), while for $Φ<Φ_c$ superconductivity arises for arbitrarily weak attraction, with a BCS-like exponential scaling of the gap due to the finiteness of the density of states. Close to the transition, we study the scaling behavior and identify the critical exponents. Our results highlight the interplay between magnetic band topology and attractive pairing in three-dimensional Hofstadter systems. |
| title | Superconducting properties of the three-dimensional Hofstadter-Hubbard model below the critical flux for Weyl points |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2604.19332 |