Time-dependent Ginzburg-Landau treatment of rf magnetic vortices in superconductors: Vortex semiloops in a spatially nonuniform magnetic field

In this paper, based on the time-dependent Ginzburg–Landau theory, we study the dynamics of vortex–antivortex (V–Av) pairs in a mesoscopic superconducting square with a small hole under applied bias currents. For the sample with a centered hole, a V–Av pair can nucleate at the hole edges and moves in opposite directions perpendicular to applied constant DC drive. The influence of the external magnetic field on the (anti)vortex velocity and the lifetime of V–Av pairs is mainly investigated. Different modes in the dynamical process of the V–Av collision and annihilation are identified. Moreover, in the case when the hole is displaced from the center of the square, the V–Av dynamics behaves quite differently from the symmetric case due to the shift of the V–Av creation point.

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Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity

Abstract and Applied Analysis ◽

10.1155/aaa.2005.863 ◽

2005 ◽

Vol 2005 (8) ◽

pp. 863-887

Author(s):

Fouzi Zaouch

Keyword(s):

Magnetic Field ◽

Existence And Uniqueness ◽

Uniform Boundedness ◽

Strong Solutions ◽

Time Dependent ◽

Dynamical Process ◽

Ginzburg Landau ◽

Ginzburg Landau Equations ◽

Uniformly Bounded ◽

Weak And Strong Solutions

The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic fieldHare discussed. We prove existence and uniqueness of weak and strong solutions withH1-initial data. The result is obtained under the “φ=−ω(∇⋅A)” gauge withω>0. These solutions generate a dynamical process and are uniformly bounded in time.

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TRANSPORT PHENOMENA IN THE MIXED STATE AND FLUCTUATION REGIME IN (Bi1.6Pb0.4)Sr2Ca1-xHox(Cu1-yZny)2O8+d

Modern Physics Letters B ◽

10.1142/s0217984901002725 ◽

2001 ◽

Vol 15 (21) ◽

pp. 929-934

Author(s):

G. ILONCA ◽

A. V. POP ◽

R. STIUFIUC ◽

G. STIUFIUC ◽

C. LUNG ◽

...

Keyword(s):

Magnetic Field ◽

Mixed State ◽

Landau Theory ◽

Hole Concentration ◽

Transport Coefficients ◽

Time Dependent ◽

Ginzburg Landau ◽

Metallic Behavior ◽

Fluctuation Effects ◽

Longitudinal Resistivity

Measurements of the magnetoresistivity, Seebeck, Nernst and Hall coefficients in Bi:2212 superconductors doped with Ho and Zn are reported. The critical temperature and the transport coefficients depend strongly on the Ho and Zn contents. The tails of the transport coefficients versus temperature curves are caused by fluctuation effects, which increase with increasing magnetic field. An anomalous suppression of superconductivity at x = 0.25–0.35 and y = 0.025–0.032 was also found when the hole concentration per Cu is P H = 1/8 and the transport properties exhibit metallic behavior. It was found that dB c2 /dT = -2.4 ± 0.2 T/K , corresponding to a Ginzburg–Landau coherence length ξ = 15 Å. The Hall resistivity ρxy scaling with the longitudinal resistivity ρxx as [Formula: see text] with α ≈ 1.8 is in agreement with the theory of Vinokur et al. The experimental data in the mixed state are in agreement with the prediction of the time-dependent Ginzburg–Landau theory.

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Released power in a vortex-antivortex pairs annihilation process

Revista UIS Ingenierías ◽

10.18273/revuin.v20n1-2021014 ◽

2020 ◽

Vol 20 (1) ◽

Author(s):

Cristian Aguirre-Tellez ◽

Miryam Rincón-Joya ◽

José José Barba-Ortega

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Diffusion Equation ◽

Power Dissipation ◽

Time Dependent ◽

Thermal Dissipation ◽

Annihilation Process ◽

Ginzburg Landau ◽

Dissipation Process ◽

Ginzburg Landau Equations

In this paper, we studied the power dissipation process of a Shubnikov vortex-antivortex pair in a mesoscopic superconducting square sample with a concentric square defect in presence of an oscillatory external magnetic field. The time-dependent Ginzburg-Landau equations and the diffusion equation were numerically solved. The significant result is that the thermal dissipation is associated with a sizeable relaxation of the superconducting electrons, so that the power released in this kind of process might become calculated as a function of the time. Also, we analyzed the effect that the Ginbzurg-Landau κand deformation τparameters have on the magnetization, dissipate power and super-electrons density.

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Proximity effect enhancement induced by a superconducting anti-dot

Modern Physics Letters B ◽

10.1142/s021798491450242x ◽

2014 ◽

Vol 28 (31) ◽

pp. 1450242

Author(s):

Sindy J. Higuera ◽

Miryam R. Joya ◽

J. Barba-Ortega

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Proximity Effect ◽

Magnetization Curve ◽

Order Parameter ◽

Proximity Effects ◽

Time Dependent ◽

Critical Fields ◽

Ginzburg Landau ◽

Ginzburg Landau Equations

In this work, we study the proximity and pinning effects of a rectangular superconducting anti-dot on the magnetization curve of a mesoscopic sample. We solve the nonlinear time-dependent Ginzburg–Landau equations for a superconducting rectangle in the presence of a magnetic field applied perpendicular to its surface. The pinning effects are determined by the number of vortices into the anti-dot. We calculate the order parameter, vorticity, magnetization and critical fields as a function of the external magnetic field. We found that the size and nature of the anti-dot strongly affect the magnetization of the sample. The results are discussed in framework of pinning and proximity effects in mesoscopic systems.

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Ginzburg-Landau dynamics with a time-dependent magnetic field

Nonlinearity ◽

10.1088/0951-7715/11/2/006 ◽

1998 ◽

Vol 11 (2) ◽

pp. 291-305 ◽

Cited By ~ 9

Author(s):

Hans G Kaper ◽

Peter Takác

Keyword(s):

Magnetic Field ◽

Time Dependent ◽

Ginzburg Landau

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Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity

Journal of Function Spaces and Applications ◽

10.1155/2013/692879 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Mariusz Gil ◽

Stanisław Wędrychowicz

Keyword(s):

Magnetic Field ◽

Banach Space ◽

Fixed Point ◽

Global Attractivity ◽

Mild Solutions ◽

Time Dependent ◽

Ginzburg Landau ◽

Superconducting Sample ◽

Tdgl Equations ◽

Theory Of Superconductivity

We study the existence of mild solutions to the time-dependent Ginzburg-Landau ((TDGL), for short) equations on an unbounded interval. The rapidity of the growth of those solutions is characterized. We investigate the local and global attractivity of solutions of TDGL equations and we describe their asymptotic behaviour. The TDGL equations model the state of a superconducting sample in a magnetic field near critical temperature. This paper is based on the theory of Banach space, Fréchet space, and Sobolew space.

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