Boundary conditions in Ginsburg–Landau theory and critical temperature of high- superconductors

Lykov, A. N.

doi:10.1016/j.physleta.2008.04.064

Cited by 9 publications

(14 citation statements)

References 7 publications

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“…The estimations, which were made in the works [12,13] by using the method, demonstrated that the best agreement the theoretical and experimental dependencies of the critical temperature as a function of the number of superconducting CuO 2 planes was achieved for the T cm = T c (n = ∞) = 155 K. For this reason, the value of T cm is used in the present study.…”

Section: Statement Of the Problemmentioning

confidence: 74%

“…The number (n) in each unit cell varies from 1 to 3. The parameters T c and were taken close to the values used in [12,13] in which the T c (n) dependence was explained. Using the empirical formula (3) for the determination of the extrapolation length and assuming that T cs = T c (n = 1), we found that /ξ(0) = 2 for Bi-based superconductor Bi 2 Sr 2 CaCu 2 O 8 .…”

Section: Results Of the Calculationsmentioning

confidence: 99%

“…For example, the origin of the effect in the layered HTSCs is the depression of the superconducting order parameter in the tightly spaced superconducting CuO 2 planes by the neighboring insulating layers in the unit cell. The critical temperature dependence of the HTSC copper oxide superconductors as a function of the number of identical superconducting CuO 2 planes in the unit cell was explained in [12,13] by using this approach. Thus, the GLG theory is important to study of the HTSCs.…”

Section: Introductionmentioning

confidence: 99%

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The Boundary Effect on the Energy Gap of High T c Superconductors

Lykov

2017

J Supercond Nov Magn

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Spatial dependence of the pairing potential across the thickness of the superconducting CuO 2 planes in high T c superconductors (HTSC) copper oxides is found by using the Ginzburg-Landau-Gor'kov (GLG) theory. The potential turned out to be significantly suppressed due to an effect of non-superconducting layers, which separate the CuO 2 planes. The effect leads also to the reduction of the critical temperature of these superconductors. The temperature dependence of the effective energy gap was calculated in this work.

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Section: Statement Of the Problemmentioning

confidence: 74%

Section: Results Of the Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Boundary Effect on the Energy Gap of High T c Superconductors

Lykov

2017

J Supercond Nov Magn

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“…The same boundary condition (1) applies also [25][26][27][28][29] to the solution of the nonlinear Ginzburg-Landau (GL) equation [30] ∇ 2 Ψ(r) + k 2 Ψ(r) + β |Ψ(r)| 2 Ψ(r) = 0 (6) with positive GL parameter β. Despite its venerable age, phenomenological GL theory of superconductivity [30,31] continues to be a powerful tool of studying superconductors as its predictions are in a very good agreement with the experiment.…”

Section: Introductionmentioning

confidence: 99%

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Olendski¹

2012

Annals of Physics

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Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius ρ0 in the superposition of the longitudinal uniform magnetic field B and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths Λin and Λout, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part Ei of the total transverse energy E is discussed. The energy E turns real under special correlation between the imaginary parts of Λin and Λout with the opposite signs what corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy E on Λin and Λout. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy Ei is quenched by the strong intensities B, then for the annulus this takes place only when the inner Robin distance Λin is real; otherwise, it almost quadratically depends on B with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.

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“…Even though some basic equations for this geometry have been derived before, their analysis in the just cited references was limited to the linear case and nonnegative Λ only. In particular, it was shown that the critical film width d c at which the superconductivity emerges, depends on Λ as [13,21,23]…”

Section: Introductionmentioning

confidence: 99%

Influence of the interplay between de Gennes boundary conditions and cubicity of Ginzburg-Landau equation on the properties of superconducting films

Olendski¹

2012

Preprint

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Exact solutions of the Ginzburg-Landau (GL) equation for the straight film subjected at its edges to the Robin-type boundary conditions characterized by the extrapolation length Λ are analyzed with the primary emphasis on the interaction between the coefficient β of the cubic GL term and the de Gennes distance Λ and its influence on the temperature T of the strip. Very substantial role is played also the superconductivity is destroyed by the growing GL nonlinearity at some temperature T > T c , which depends on Λ, n s and β. It is proved that the concentration n (0) s transforms for the large cubicities into the density of the bulk sample.

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Boundary conditions in Ginsburg–Landau theory and critical temperature of high- superconductors

Cited by 9 publications

References 7 publications

The Boundary Effect on the Energy Gap of High T c Superconductors

The Boundary Effect on the Energy Gap of High T c Superconductors

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Influence of the interplay between de Gennes boundary conditions and cubicity of Ginzburg-Landau equation on the properties of superconducting films

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