The Josephson Effect in Superconductive Tunneling Structures

Kulik, I. O.; Yanson, I. K.; Langenberg, D. N.

doi:10.1119/1.1987851

Cited by 87 publications

(148 citation statements)

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“…13,14 , we employ a new, more general method of the derivation of topological solutions. In particular, we start with a full set of solutions to (1), (2). In contrast to the approach of Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, although the general solution to (1) was well-known, 12 the constants of integration specifying all physically observable configurations could not be unambiguously determined from boundary conditions (2) alone.…”

Section: Introductionmentioning

confidence: 99%

“…(1), (2) are nothing but stationarity conditions of a relevant Gibbs free-energy functional. 13,14 Therefore, among all solutions to (1) that satisfy The geometry of the problem: t is the thickness of the barrier; W = 2L is the length of the barrier; λ is the London penetration depth; d = 2λ + t is the width of the field-penetration region (shaded).…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, equations (1), (2) constitute an ill-posed boundary-value problem 11 in the sense that they do not meet the requirement of the uniqueness of the solution. [This is a consequence of nonlinearity of Eq.…”

Section: Introductionmentioning

confidence: 99%

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Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions

Kuplevakhsky

Glukhov

2006

Phys. Rev. B

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The problem of vortex structure in a single Josephson junction in an external magnetic field, in the absence of transport currents, is reconsidered from a new mathematical point of view. In particular, we derive a complete set of exact analytical solutions representing all the stationary points (minima and saddle-points) of the relevant Gibbs free-energy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs free-energy functional. The stable (physical) solutions minimizing the Gibbs free-energy functional form an infinite set and are labelled by a topological number Nv = 0, 1, 2, . . .. Mathematically, they can be interpreted as nontrivial "vacuum" (Nv = 0) and static topological solitons (Nv = 1, 2, . . .) of the sine-Gordon equation for the phase difference in a finite spatial interval: solutions of this kind were not considered in previous literature. Physically, they represent the Meissner state (Nv = 0) and Josephson vortices (Nv = 1, 2, . . .). Major properties of the new physical solutions are thoroughly discussed. An exact, closed-form analytical expression for the Gibbs free energy is derived and analyzed numerically. Unstable (saddle-point) solutions are also classified and discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions

Kuplevakhsky

Glukhov

2006

Phys. Rev. B

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“…From measurements of the current-voltage (I-V ) characteristics, Langenberg et al [3] found the power P = IV fed into the junction and the fraction converted into radiation, Q = P rad /P ≈ 10 −5 . Theoretically Q was estimated as a ratio of the impedances of JJ modeled as a strip line and the waveguide [3,5]:…”

Section: Introductionmentioning

confidence: 99%

Radiation from Flux Flow in Josephson Junction Structures

Bulaevskiǐ

Koshelev

2006

J Supercond

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We derive the radiation power from a single Josephson junction (JJ) and from layered superconductors in the flux-flow regime. For the JJ case we formulate the boundary conditions for the electric and magnetic fields at the edges of the superconducting leads using the Maxwell equations in the dielectric media and find dynamic boundary conditions for the phase difference in JJ which account for the radiation. We derive the fraction of the power fed into JJ transformed into the radiation. In a finite-length JJ this fraction is determined by the dissipation inside JJ and it tends to unity as dissipation vanishes independently of mismatch of the junction and dielectric media impedances. We formulate also the dynamic boundary conditions for the phase difference in intrinsic Josephson junctions in highly anisotropic layered superconductors of the Bi 2 Sr 2 CaCu 2 O 8 type at the boundary with free space. Using these boundary conditions, we solve equations for the phase difference in the linear regime of Josephson oscillations for rectangular and triangular lattices of Josephson vortices. In the case of rectangular lattice for crystals with the thickness along the c-axis much larger than the radiation wavelength we estimate the radiation power per unit length in the direction of magnetic field at the frequency 1 THz as ∼ N µW/cm for Tl 2 Ba 2 CaCu 2 O 8 and ∼ 0.04 N µW/cm for Bi 2 Sr 2 CaCu 2 O 8 . For crystals with thickness smaller than the radiation wavelength we found that the radiation power in the resonance is independent on number of layers and can be estimated at 1 THz as 0.5 W/cm (Tl 2 Ba 2 CaCu 2 O 8 ) and 24 mW/cm (Bi 2 Sr 2 CaCu 2 O 8 ). For rectangular lattice, due to superradiation regime, up to half of power fed into the crystal may be converted into the radiation. In the case of triangular or random lattice in the direction perpendicular to the layers the fraction of power converted into the radiation depends on the dissipation rate and is much lower than for rectangular lattice in the case of high-temperature superconductors with nodes in the gap.

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Diffraction and interference phenomena in single Josephson junctions

Barone

Paternò

Russo³

et al. 1977

Phys. Stat. Sol. (a)

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The influence of non uniform tunnelling current distribution in "small" Josephson junctions is discussed. Experimental results on the magnetic field dependence of the critical current are reported for various kinds of structures. The whole analysis of the data gives interesting conclusions and indicates procedures of diagnostic interest.Es wird der EinfluB einer nichtgleichformigen Verteilung des Tunnelstromes in ,,schmalen" Josephson-Ubergangen diskutiert. Es werden experimentelle Ergebnisse der magnetischen Feldabhangigkeit des kritischen Stromes fur verschiedene Arten der Struktur mitgeteilt. Die gesamte Analyse der Daten ergibt interessante Schliisse und Hinweise fur interessierende Diagnoseverfahren.

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The Josephson Effect in Superconductive Tunneling Structures

Cited by 87 publications

References 0 publications

Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions

Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions

Radiation from Flux Flow in Josephson Junction Structures

Diffraction and interference phenomena in single Josephson junctions

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