Mesoscopic Josephson effect in graphene disk at magnetic field
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913062656671744 |
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| author | Rycerz, Adam |
| author_facet | Rycerz, Adam |
| contents | Unlike for tunneling Josephson junctions, for which the current-phase relation is given by the sine function, with the critical current ($I_c$) and normal-state resistance ($R_N$) following the relation $I_cR_N=(π/2)\,Δ_0/e$ (where $Δ_0$ is the superconducting gap and electron charge is $-e$), mesoscopic Josephson junctions show more complex current-phase relations, with the skewness $S>0$, what is related to the presence -- in case the leads are in the normal state -- of transmission probabilities taking the values comparable to $1$. Here, we show that these features also appear for a superconductor-graphene-superconductor (S-g-S) junction in the disk-shaped (Corbino) geometry, when the magnetic field is adjusted such that $I_c\rightarrow{}0$ and $R_N\rightarrow{}\infty$. In such a case, the product $I_cR_N\approx{}1.85\,Δ_0/e$, and the skewness $S\approx{}0.14$. The results obtained from quantum-mechanical mode-matching analysis for the Dirac-Bogoliubov-De-Gennes equation are compared with simpler model assuming incoherent scattering between two circular interfaces separating the sample and the leads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mesoscopic Josephson effect in graphene disk at magnetic field Rycerz, Adam Mesoscale and Nanoscale Physics Superconductivity Unlike for tunneling Josephson junctions, for which the current-phase relation is given by the sine function, with the critical current ($I_c$) and normal-state resistance ($R_N$) following the relation $I_cR_N=(π/2)\,Δ_0/e$ (where $Δ_0$ is the superconducting gap and electron charge is $-e$), mesoscopic Josephson junctions show more complex current-phase relations, with the skewness $S>0$, what is related to the presence -- in case the leads are in the normal state -- of transmission probabilities taking the values comparable to $1$. Here, we show that these features also appear for a superconductor-graphene-superconductor (S-g-S) junction in the disk-shaped (Corbino) geometry, when the magnetic field is adjusted such that $I_c\rightarrow{}0$ and $R_N\rightarrow{}\infty$. In such a case, the product $I_cR_N\approx{}1.85\,Δ_0/e$, and the skewness $S\approx{}0.14$. The results obtained from quantum-mechanical mode-matching analysis for the Dirac-Bogoliubov-De-Gennes equation are compared with simpler model assuming incoherent scattering between two circular interfaces separating the sample and the leads. |
| title | Mesoscopic Josephson effect in graphene disk at magnetic field |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2604.23470 |