Correction to the Josephson current in the second order of perturbation theory in the transparency

Antsygina, T. N.; Svidzinskii, A. V.

doi:10.1007/bf01029313

Theor Math Phys

1973

DOI: 10.1007/bf01029313

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Correction to the Josephson current in the second order of perturbation theory in the transparency

T. N. Antsygina¹,

A. V. Svidzinskii²

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1987

2022

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Cited by 5 publications

(2 citation statements)

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“…The sign of jc1 coincides with the sign of g ℓ , while the sign of j c2 is determined by the sign of g δ . For small pair breaking 0 < g δ ≪ 1 the second order term ∝ g 2 ℓ is simplified to the following correction to the current − √ 2j c0 g ℓ (sin χ − (1/2) sin 2χ), in agreement with the corresponding microscopic results 16,40 for dirty and pure s-wave junctions. Note that the phase dependence generated by the current depairing shows up in (4) beginning with the third order terms in g ℓ .…”

supporting

confidence: 82%

Anharmonic Josephson current in junctions with an interface pair breaking

Barash

2012

Phys. Rev. B

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Planar superconducting junctions with a large effective Josephson coupling constant and a pronounced interface pair breaking are shown to represent weak links with small critical currents and strongly anharmonic current-phase relations. The supercurrent near Tc is described taking into account the interface pair breaking as well as the current depairing and the Josephson coupling-induced pair breaking of arbitrary strengths. A new analytical expression for the anharmonic supercurrent, which is in excellent agreement with the numerical data presented, is obtained. In junctions with a large effective Josephson coupling constant and a pronounced interface pair breaking, the currentinduced depairing is substantially enhanced in the vicinity of the interface thus having a crucial influence on the current-phase relation despite a small depairing in the bulk. The Josephson current is one of the remarkable manifestations of quantum coherence on the macroscopic scale in condensed matter physics. The supercurrent depends on the phase difference of the order parameters across the junction interface. The study of the current-phase relation (CPR) in the junctions makes it possible to identify physical processes, which form supercurrents under diverse conditions. It is also beneficial for junction applications. The problem attracted much attention while studying both highly transparent junctions with strongly anharmonic CPRs and tunnel junctions, where the second harmonic of the supercurrent comes into play due to the suppression of the first one 1-10 . The latter takes place in the junctions involving unconventional superconductors with special interface-to-crystal orientations and at 0-π transitions.One of the earlier theoretical results, clarifying a variety of aspects of the problem, is the anharmonic CPR for the superconducting point contacts [11][12][13][14][15] . Due to the negligibly small current-induced pair breaking at any transparency value, the theory of point contacts is simplified. The depairing plays an important role in forming anharmonic CPRs in highly transparent planar junctions, unlike its negligible role in point contacts. Since the critical current j c of usual planar junctions becomes, with increasing transparency, comparable with the depairing current j dp in the bulk, the junctions do not represent weak links. In other words, in the junctions, the current-induced depairing brings about a pronounced anharmonicity only in the crossover from the tunnel Josephson current to the bulk superflow 1,16-18 .There are at least three types of pair breaking processes taking place in charge transport in the superconducting junctions: the pair breaking produced by the phase-dependent Josephson coupling, by the current and by the interface itself. These are the very same effects which can lead to a noticeably anharmonic CPR not only at low or intermediate temperatures, but also near T c . Here, I show that planar junctions with a large effective Josephson coupling constant and a pronounced interface pair breaking ca...

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supporting

confidence: 82%

Anharmonic Josephson current in junctions with an interface pair breaking

Barash

2012

Phys. Rev. B

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“…In the 1D geometry (e.g., a planar junction or a superconducting channel with a tunnel barrier [4]), the problem is complicated considerably due to the change in the order parameter and the quasiparticle energy spectrum in the vicinity of the junction, which makes a contribution to the phase dependence of the current j(Φ). Antsygina and Svidzinskii [5] determined the corresponding corrections to j(Φ) of the order of Γ 2 for a pure (l ≫ ξ 0 ) superconductor in the limit of low transmissivity Γ ≪ 1:…”

mentioning

confidence: 99%

On the theory of Josephson effect in a diffusive tunnel junction

Bezuglyĭ

Bratus

Galaiko

1999

Low Temperature Physics

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Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors are studied theoretically in the 1D geometry. It is found that the Josephson current induces localized states of electron excitations in the vicinity of the tunnel barrier, which are a continuous analog of Andreev levels in a ballistic junction. The depth of the corresponding ``potential well'' is much greater than the separation between an Andreev level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic junction in which the Josephson current is transported completely by localized excitations, the contribution to current in a diffusive junction comes from whole spectral region near the energy gap boundary, where the density of states differs considerably from its unperturbed value. The correction to the Josephson current in the second order of the barrier transmissivity, which contains the second harmonic of the phase jump, is calculated and it is found that the true expansion parameter of the perturbation theory for a diffusive junction is not the tunneling probability $\Gamma$ itself, but a much larger parameter $W = (3\xi_0/4l)\Gamma$.Comment: 8 pages, 5 Postscript figures, submitted to Low Temp. Phy

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Microscopic theory of nonstationary tunnel current in a superconducting junction

Akhramovich¹,

Svidzinskii²

1987

Theor Math Phys

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Correction to the Josephson current in the second order of perturbation theory in the transparency

Cited by 5 publications

References 3 publications

Anharmonic Josephson current in junctions with an interface pair breaking

Anharmonic Josephson current in junctions with an interface pair breaking

On the theory of Josephson effect in a diffusive tunnel junction

Microscopic theory of nonstationary tunnel current in a superconducting junction

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