scholarly journals The Ginzburg--Landau Order Parameter near the Second Critical Field

2014 ◽  
Vol 46 (1) ◽  
pp. 572-587 ◽  
Author(s):  
Ayman Kachmar
Keyword(s):  
Critical Field ◽  
Order Parameter ◽  
Ginzburg Landau ◽  
Second Critical Field

ON THE SECOND CRITICAL FIELD FOR A GINZBURG–LANDAU MODEL WITH FERROMAGNETIC INTERACTIONS

2004 ◽  
Vol 16 (02) ◽  
pp. 147-174 ◽  
Author(s):  
STAN ALAMA ◽  
LIA BRONSARD
Keyword(s):  
Magnetic Field ◽  
Critical Field ◽  
Order Parameter ◽  
Upper Critical Field ◽  
Average Energy ◽  
Spin Coupling ◽  
P Wave ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Second Critical Field

We consider a two-dimensional Ginzburg–Landau model for superconductors which exhibit ferromagnetic ordering in the superconducting phase, introduced by physicists to describe unconventional p-wave superconductors. In this model the magnetic field is directly coupled to a vector-valued order parameter in the energy functional. We show that one effect of spin coupling is to increase the second critical field Hc2, the value of the applied magnetic field at which superconductivity is lost in the bulk. Indeed, when the spin coupling is strong we show that the upper critical field is no longer present, confirming predictions in the physics literature. We treat the energy density as a measure, and show that the order parameter converges (as the Ginzburg–Landau parameter κ→∞) in an average sense to a constant determined by the average energy.

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 Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

Ginzburg–Landau theory of the Abrikosov vortex state near the upper critical field

1982 ◽  
Vol 60 (3) ◽  
pp. 299-303 ◽  
Author(s):  
A. E. Jacobs
Keyword(s):  
Critical Field ◽  
Landau Theory ◽  
Upper Critical Field ◽  
Vortex State ◽  
Quantization Condition ◽  
Abrikosov Vortex ◽  
Ginzburg Landau ◽  
Type Ii Superconductors ◽  
Flux Quantization ◽  
The Magnetic Field

A method which preserves the flux-quantization condition in all orders of perturbation theory is applied to the Ginzburg–Landau theory of type-II superconductors near the upper critical field. Expansions are obtained for the order parameter, the magnetic field, and the free energy; previous results are verified and extended to one higher order in Hc2 – Ha.

scholarly journals The distribution of 3D superconductivity near the second critical field

Nonlinearity ◽  
2016 ◽  
Vol 29 (9) ◽  
pp. 2856-2887 ◽  
Author(s):  
Ayman Kachmar ◽  
Marwa Nasrallah
Keyword(s):  
Critical Field ◽  
Second Critical Field
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