Investigation of the superconducting proximity effect by Josephson tunneling

1976 ◽  
Vol 54 (3) ◽  
pp. 223-226 ◽  
Author(s):  
N. L. Rowell ◽  
H. J. T. Smith
Keyword(s):  
Simple Model ◽  
Proximity Effect ◽  
Order Parameter ◽  
Landau Equation ◽  
The Other ◽  
Superconducting Layer ◽  
Ginzburg Landau ◽  
Josephson Tunneling ◽  
Superconducting Proximity Effect

Josephson junctions have been made with a superconductor on one side of the oxide and with a normal–superconducting (N–S) sandwich on the other side. Measurements of the temperature dependence of the maximum DC Josephson current have been taken.A simple model is proposed for the order parameters within the N–S system. Within the superconducting layer of this system the linear Ginzburg–Landau equation is used to describe the behavior of the order parameter. Within the normal metal, Werthamer's solution is used. Application of de Gennes' boundary conditions completes the determination of the order parameter. Josephson currents are calculated by using the de Gennes formulation. Agreement between experiment and theory has been obtained.

scholarly journals Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Anatoly A. Barybin
Keyword(s):  
Order Parameter ◽  
Continuity Equation ◽  
Chemical Potential ◽  
Landau Equation ◽  
Time Dependent ◽  
Quantum Dissipation ◽  
Ginzburg Landau ◽  
Superfluid Component ◽  
Ginzburg Landau Equation ◽  
Conservation Property

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.

scholarly journals Finite-size effects in metallic superlattice systems

1995 ◽  
Vol 73 (9-10) ◽  
pp. 545-553
Author(s):  
J. Chen ◽  
R. Kobes ◽  
J. Wang
Keyword(s):  
Critical Temperature ◽  
Simple Model ◽  
Proximity Effect ◽  
Size Effects ◽  
Finite Size ◽  
Cooper Pairs ◽  
Superconducting Layer ◽  
Finite Size Effects ◽  
Realistic Form ◽  
Pair Amplitude

Clean metallic superlattice systems composed of alternating layers of superconducting and normal materials are considered, particularly aspects of the proximity effect as it affects the critical temperature. A simple model is used to address the question of when a finite–sized system theoretically approximates well a true infinite superlattice. The methods used in the analysis afford some tests of the approximation used that the pair amplitude of the Cooper pairs is constant over a superconducting region. We also use these methods to construct a model of a single superconducting layer which intends to incorporate a more realistic form of the pair amplitude than a simple constant.

scholarly journals Bounded solutions for an ordinary differential system from the Ginzburg–Landau theory

2020 ◽  
Vol 150 (6) ◽  
pp. 3378-3408
Author(s):  
Anne Beaulieu
Keyword(s):  
Bounded Solution ◽  
Landau Theory ◽  
Landau Equation ◽  
The Other ◽  
Two Dimensional ◽  
Bounded Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Specific Contribution ◽  
Solution Problem

In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg–Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the Ginzburg–Landau equation by translations and rotations. The specific contribution of our work is to prove that in the other cases, the system does not admit any bounded solutions. We show that this bounded solution problem is related to an eigenvalue problem.

scholarly journals Asymptotic analysis of a new type of multi-bump, self-similar, blowup solutions of the Ginzburg–Landau equation

2012 ◽  
Vol 24 (1) ◽  
pp. 103-129 ◽  
Author(s):  
V. ROTTSCHÄFER
Keyword(s):  
Asymptotic Analysis ◽  
Landau Equation ◽  
Asymptotic Methods ◽  
Geometric Construction ◽  
The Other ◽  
Ginzburg Landau ◽  
Geometric Methods ◽  
Ginzburg Landau Equation ◽  
New Type ◽  
Self Similar

We study of a new type of multi-bump blowup solutions of the Ginzburg–Landau equation. Multi-bump blowup solutions have previously been found in numeric simulations, asymptotic analysis and were proved to exist via geometric construction. In the geometric construction of the solutions, the existence of two types of multi-bump solutions was shown. One type is exponentially small at ξ=0, and the other type of solutions is algebraically small at ξ=0. So far, the first type of solutions were studied asymptotically. Here, we analyse the solutions which are algebraically small at ξ=0 by using asymptotic methods. This construction is essentially different from the existing one, and ideas are obtained from the geometric construction. Hence, this is a good example of where both asymptotic analysis and geometric methods are needed for the overall picture.

Proximity effect enhancement induced by a superconducting anti-dot

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.

ENERGY EXCHANGE IN COLLISIONS BETWEEN TWO DISSIPATIVE OPTICAL BULLETS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350018
Author(s):  
XIANG ZENG ◽  
BING TANG ◽  
LIANG WANG ◽  
PENG KONG ◽  
YI TANG
Keyword(s):  
Energy Transfer ◽  
Energy Exchange ◽  
Energy Transfer Process ◽  
Landau Equation ◽  
Three Dimensional ◽  
Dissipative System ◽  
High Energy ◽  
The Other ◽  
Ginzburg Landau ◽  
Optical Bullets

By using the three-dimensional complex cubic-quintic Ginzburg-Landau equation, the energy transfer process is investigated numerically for collisions of two dissipative optical bullets in a dissipative system. For high energy solitons, as a result of energy transfer, one soliton gains energy to generate a double bullet complex, and the other one loses energy can survive in collisional process. In addition, we find that the variations of the bullets velocity show regular properties during mutiple collisions with phase difference.

Time-dependent Landau theory for order/disorder processes in minerals

1989 ◽  
Vol 53 (372) ◽  
pp. 483-504 ◽  
Author(s):  
M. A. Carpenter ◽  
E. Salje
Keyword(s):  
Order Parameter ◽  
Driving Forces ◽  
Landau Theory ◽  
Landau Equation ◽  
Excess Entropy ◽  
Time Dependent ◽  
Specific Rate ◽  
Ginzburg Landau ◽  
Rate Laws ◽  
Image Position

AbstractRecent advances in the use of time-dependent order parameter theory to describe the kinetics of order/disorder transitions are reviewed. The time dependence of a macroscopic order parameter, Q, follows, to a good approximation:For systems in which the order parameter has a long correlation length (large ξ) and is not conserved (small ξC), the Ginzburg-Landau equation provides a general kinetic solution:Specific rate laws can be derived from this general solution depending on whether the crystals remain homogeneous with respect to the order parameter, Q. The advantages of the overall approach are, firstly, that it does not depend on the detailed structure of the material being examined; secondly, that the order parameter can be followed experimentally through its relationship with other properties, such as spontaneous strain, excess entropy, intensities of superlattice reflections, etc.; and, finally, that conventional Landau expansions in Q may be used to describe the thermodynamic driving forces.For a simple second-order transition in crystals which remain homogeneous in Q the rate law is:If the free energy of activation varies with the state of order of the crystal, this becomes:Simplifying assumptions can be introduced into the mathematics, or the integrals can be solved numerically. For crystals which remain homogeneous, the simplest solution valid only over small deviations from equilibrium is:For crystals which develop heterogeneities in Q, the rate laws change significantly and we find as an extreme case:where the A coefficient may be temperature dependent.Experimental data available for a limited number of minerals (omphacite, anorthite, albite, cordierite and nepheline) are used to demonstrate the practical implications of the overall approach. As anticipated from the theory, modulated structures commonly develop during kinetic experiments, the observed rate laws depend on whether the critical point of the ordering is located at the centre or boundary of the Brillouin zone, and the rate laws for ordering and disordering can be quite different. The importance of different length scales, not only in the different techniques for characterizing states of order (IR, NMR, calorimetry, X-ray diffraction, etc.) but also for interpreting observed mechanisms and rate laws, is also outlined.Use of the order parameter in Landau expansions and in Ginzburg-Landau rate laws provides, in principle, a means of predicting the equilibrium and non-equilibrium evolution of minerals in nature.

A Ginzburg-Landau equation with non-local correction for superconductors in zero magnetic field

1973 ◽  
Vol 334 (1597) ◽  
pp. 171-192 ◽  
Keyword(s):  
Magnetic Field ◽  
Numerical Calculation ◽  
Order Parameter ◽  
Landau Theory ◽  
Landau Equation ◽  
Zero Magnetic Field ◽  
Ginzburg Landau ◽  
Local Correction ◽  
Non Local ◽  
The One

A form of Ginzburg-Landau theory with non-local correction is derived which is useful in numerical calculation of the spatial variation of the order parameter for superconductors in zero magnetic field. This form of theory is obtained as an extension of the low-temperature modifications of G-L theory developed by Werthamer and others, and is valid over a considerably wider range of values of temperature and order parameter. Boundary conditions at the interface between two metals applicable under rather general conditions are obtained, and the numerical calculation of the one-electron eigenstates in the presence of a spatially varying order parameter is discussed briefly in an appendix.

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