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Concepts and Principal Provisions of Fundamental and Applied Superconductivity
Published in V.R. Romanovskii, Basic Macroscopic Principles of Applied Superconductivity, 2021
In 1950, Ginzburg and Landau (Ginzburg and Landau 1950) proposed the theory using thermodynamic concepts. It is based on Landau’s theory of the phase transitions of the second-order to predict the superconducting electron density ns. The Ginzburg-Landau equations lead to the characteristic parameter κ = λL/ξ, which is equal to the ratio of the penetration depth λL and the coherence length ξ;. The latter quantity may be defined as the length scale over which Ginzburg-Landau’s order factor varies. The coherence length is also a measure of the length scale over which the gradual change from normal to superconducting state occurs at the external boundary of a superconductor. Therefore, it can be considered as the scale over which the superconducting electron of the density ns goes from zero at the external boundary to a constant value inside the superconductor. The Ginzburg-Landau theory is an alternative to London’s theory. However, the Ginzburg-Landau theory does not explain the microscopic mechanisms of superconductivity. It examines the macroscopic properties of the superconductor with the aid of general thermodynamic equations. This theory is the phenomenological theory in the sense of its assumptions for describing the state transition. It is based on quantum mechanics instead of the macroscopic electromagnetic phenomena.
Existence and Duality Principles for the Ginzburg-Landau System in Superconductivity
Published in Fabio Silva Botelho, Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering, 2020
In particular, from the Ginzburg-Landau theory for the dimensionless case we have, γ= 1, γ=1,α=12(1+t2)2and ß = 1 – t4, where t = T /Tc, Tc is the critical temperature and T is the super-conducting sample actual one. A typical value for t is t = 0.95. Finally, the value 1/(8π) may also vary according to type of material or type of superconductor.
A Comparison of the Properties of Superconductors and Superfluid Helium
Published in R. D. Parks, Superconductivity, 2018
A phenomenological theory for the stationary states of Ψ near the λ-point in helium has been proposed by Ginzburg and Pitaevskii (23). It is exactly analogous to the phenomenological Ginzburg-Landau theory in superconductivity. The condensate wave function is treated as an order parameter, it is assumed that near the λ-point (where Ψ is small) the free energy of the system can be expanded in a power series in |Ψ|2 and |∇ψ|2 and it is assumed that ρs is proportional to | Ψ |2. It is then found that () (ℏ2/2m)∇2ψ+αψ−β|ψ|2ψ=0
Landau theory for isotropic, nematic, smectic-A, and smectic-C phases
Published in Liquid Crystals, 2020
Dora Izzo, Mário J. De Oliveira
Molecular theories can successfully describe phase transitions occurring in liquid crystals [1–13]. The same can be said about the Landau theory of phase transitions [14], which is close related to the molecular theories [15,16], and has also been applied to construct phase diagrams of liquid crystals [17–25]. The Landau theory consists in setting up a polynomial form for the free energy in terms of order parameters that describe the possible thermodynamic phases. Each term appearing in the polynomial is invariant under all transformations that leave the corresponding phases unaffected. Thus, the determining factor in the establishment a Landau free energy concerns the appropriate definition of the order parameter of each phase together with its symmetry operations.
High-throughput analysis of magnetic phase transition by combining table-top sputtering, photoemission electron microscopy, and Landau theory
Published in Science and Technology of Advanced Materials: Methods, 2022
T. Nishio, M. Yamamoto, T. Ohkochi, D. Nanasawa, A. L. Foggiatto, M. Kotsugi
Finally, we remark on the importance of Landau theory for exploring material functions and materials informatics. Landau theory explains the ferromagnetic/paramagnetic phase transition based on statistical physics. It provides us with the conditions (composition and temperature) exhibiting ferromagnetism and is useful for searching the functional magnetic materials. From the viewpoint of material informatics, this study draws a phase diagram using image information at once. We discussed the information recorded in each pixel to describe the pseudo-free energy and analysed the magnetic-phase transition based on Landau theory.