Absence of "fractional ac Josephson effect" in superconducting junctions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910657738178560 |
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| author | Kalenkov, Mikhail S. Zaikin, Andrei D. |
| author_facet | Kalenkov, Mikhail S. Zaikin, Andrei D. |
| contents | We develop a microscopic theory of ac Josephson effect in superconducting junctions described by an arbitrary scattering matrix that may include magnetic effects. In the limit of constant in time bias voltage $V$ applied to the junction we derive a formally exact current-phase relation (CPR) that is manifestly $2π$-periodic in the Josephson phase $φ$ in full accordance with general principles. This our result unambiguously argues against the idea of the so-called "fractional ac Josephson effect" admitting $4π$-periodic in $φ$ CPR. We also demonstrate that at any non-zero $V$ quantum dynamics of Andreev bound states becomes non-Hermitian which signals their instability, thus making any 'quasi-equilibrium' description of ac Josephson effect unreliable. We specifically address the limit of highly transparent junctions with magnetic scattering where -- along with super- and excess current terms -- at small $V$ we also recover a non-trivial $2π$-periodic dissipative current with the amplitude $\propto |V|^{1/3}$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Absence of "fractional ac Josephson effect" in superconducting junctions Kalenkov, Mikhail S. Zaikin, Andrei D. Superconductivity Strongly Correlated Electrons We develop a microscopic theory of ac Josephson effect in superconducting junctions described by an arbitrary scattering matrix that may include magnetic effects. In the limit of constant in time bias voltage $V$ applied to the junction we derive a formally exact current-phase relation (CPR) that is manifestly $2π$-periodic in the Josephson phase $φ$ in full accordance with general principles. This our result unambiguously argues against the idea of the so-called "fractional ac Josephson effect" admitting $4π$-periodic in $φ$ CPR. We also demonstrate that at any non-zero $V$ quantum dynamics of Andreev bound states becomes non-Hermitian which signals their instability, thus making any 'quasi-equilibrium' description of ac Josephson effect unreliable. We specifically address the limit of highly transparent junctions with magnetic scattering where -- along with super- and excess current terms -- at small $V$ we also recover a non-trivial $2π$-periodic dissipative current with the amplitude $\propto |V|^{1/3}$ |
| title | Absence of "fractional ac Josephson effect" in superconducting junctions |
| topic | Superconductivity Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.07344 |