Use of the modified Ginzburg–Landau equations in high temperature superconductors (original) (raw)
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Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors
Phys. Rev. B, 2016
We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ=λ/ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB2 suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter κ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and κ, showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.
Study of Anisotropy Superconductor using Time-Dependent Ginzburg-Landau Equation
Journal of Natural Sciences Research, 2013
We have observed an anisotropy superconductor which was immersed in vacuum medium in presence of an applied magnetic field. The anisotropy properties of superconductor were related with two principal values of the effective mass of the Cooper pairs, namely m c along the x-axis and m ab in the yz-plane. Based on the timedependent Ginzburg-Landau and yU methods, the problem was solved and made to be the numerical simulation. From study using this numerical simulation, we can find that the anisotropy properties can make the critical field to be lower or higher.
Superheating field of superconductors within Ginzburg-Landau theory
Physical Review B, 2011
We study the superheating field of a bulk superconductor within Ginzburg-Landau theory, which is valid near the critical temperature. We calculate, as functions of the Ginzburg-Landau parameter κ, the superheating field H sh and the critical momentum kc characterizing the wavelength of the instability of the Meissner state to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for an ordinary differential equation, we solve the problem numerically. We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large κ. We discuss the implications of the results for superconducting RF cavities used in particle accelerators.
Numerical Approach in Superconductivity
2020
The dependence of the critical temperature of high temperature superconductors of various families on their composition and structure is proposed. A clear dependence of the critical temperature of high temperature superconductors on the sequence number of the constituent elements, their valency, and the structure of the crystal lattice is revealed.
Ginzburg-Landau theory of type II superconductors in magnetic field
Reviews of modern physics, 2010
Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg -Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor -normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high Tc materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg -Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose -Einstein condensate. A. GL equations. 49 B. Theory of thermal fluctuations in GL model 50 C. The effects of quenched disorder 52 D. Other fields of physics 53 E. Acknowledgments 53 VI. Appendices 53 A. Integrals of products of the quasimomentum eigenfunctions 53 1. Rhombic lattice quasimomentum functions 53 2. The basic Fourier transform formulas 53 3. Calculation of the β k , γ k functions and their small momentum expansion 54 B. Parisi algebra for hierarchial matrices 56
Boundary condition for Ginzburg-Landau theory of superconducting layers
Physical Review B, 2009
Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.
. This article is concerned with the Ginzburg--Landau (GL) equations of superconductivity. The equations provide a mathematical model for the study of magnetic flux vortices in superconductors. The focus is on the asymptotic case when the charge of the superconducting charge carriers (Cooper pairs) is vanishingly small and the applied magnetic field approaches the upper critical field. It is shown that the GL model reduces in the limit to the frozen-field model, where the superconducting phenomena are affected by the electromagnetic phenomena, but not vice versa. The convergence is second order in the small parameter. The analytical results are confirmed in some numerical examples. 1 Introduction Superconducting materials hold great promise for technological applications. Especially since the discovery of the so-called high-temperature superconductors in the 1980s, much research has been devoted to understanding the behavior of these new materials. While conventional superconductors...
Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity
Sov. Phys. JETP, 1959
It is shown that the phenomenological Ginzburg-Landau equations follow from the theory of superconductivity in the London temperature region in the neighborhood of Tc. In these equa tions there occurs, however, twice the electronic charge; this is related to the physical mean ing of '1t(x) as the wave function for Cooper pairs. The constant K turns out to be small. The problem of the surface energy for the boundary between the normal and superconducting phases in the neighborhood of Tc is discussed.
An extended Ginzburg‐Landau description for superconductors
AIP Conference Proceedings, 2005
We give a straightforward generalization of the Ginzburg-Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb-Ramond field. While the standard properties of superconductors are recovered for temperatures not very far from the critical one, we predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity. A physical scenario behind the model proposed, which can be directly tested by experiments, is envisaged.