Josephson current through the SYK model
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917814079586304 |
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| author | Dell'Anna, Luca |
| author_facet | Dell'Anna, Luca |
| contents | We calculate the equilibrium Josephson current through a disordered interacting quantum dot described by a Sachdev-Ye-Kitaev model fully contacted by two BCS superconductors, such that all modes of the dot contribute to the coupling, which encodes hopping and spin-flip processes. We show that, at zero temperature and at the conformal limit, i.e. in the strong interacting limit, the Josephson current is suppressed by $U$, the strength of the interaction, as $\ln(U)/U$ and becomes universal, namely it gets independent on the superconducting gap. At finite temperature, instead, it depends on the ratio between the gap and the temperature. A proximity effect exists but the self-energy corrections induced by the coupling with the superconducting leads seem subleading as compared to the interaction self-energy and the tunneling matrix for large number of particles. Finally we compare the results of the original four-fermion model with those obtained considering zero interaction, two-fermions and a generalized q-fermion model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Josephson current through the SYK model Dell'Anna, Luca Strongly Correlated Electrons Mesoscale and Nanoscale Physics Superconductivity High Energy Physics - Theory We calculate the equilibrium Josephson current through a disordered interacting quantum dot described by a Sachdev-Ye-Kitaev model fully contacted by two BCS superconductors, such that all modes of the dot contribute to the coupling, which encodes hopping and spin-flip processes. We show that, at zero temperature and at the conformal limit, i.e. in the strong interacting limit, the Josephson current is suppressed by $U$, the strength of the interaction, as $\ln(U)/U$ and becomes universal, namely it gets independent on the superconducting gap. At finite temperature, instead, it depends on the ratio between the gap and the temperature. A proximity effect exists but the self-energy corrections induced by the coupling with the superconducting leads seem subleading as compared to the interaction self-energy and the tunneling matrix for large number of particles. Finally we compare the results of the original four-fermion model with those obtained considering zero interaction, two-fermions and a generalized q-fermion model. |
| title | Josephson current through the SYK model |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Superconductivity High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.17366 |