This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. Historically, gl theory was an extension of the landau theory of secondorder phase transitions3 onto the quantum phenomenon of superconductivity. Mathematical models and numerical simulations of superconductivity. Perfect conductivity below a critical tc, electrical resistance becomes zero infinite conductance. The ginzburg landau theory 9 provides a theoretical basis for the distinction between the two types. In physics, ginzburglandau theory, often called landauginzburg theory, named after vitaly. Introduction superconductivity refers to a complex of phenom. What sets this book apart from others on the introduction to superconductivity and high t c materials is its simple and pragmatic approach. Discovery of superconductivity, the bcs theory, ginzburglandau theory, andreev reflection, current in superconducting junctions, josephson effect and weak links, quantum phenomena in josephson junctions, unconventional superconductivity. The first part of the text concerns fluctuation phenomena that can be studied within the framework of the ginzburglandau theory of superconductivity. More than 20 metallic elements can become super conductors table 34. Niicroscopic derivation of the ginzburglandau equations. And it encompasses two rich topics within super conductivity i josephson junctions, and ii the abrikosov vortexlattice phase of.
The ginzburglandau free energy functional of color superconductivity at weak coupling ioannis giannakisa and haicang rena y aphysics department, the rockefeller university 1230 york avenue, new york, ny 100216399 abstract we derive the ginzburglandau free energy functional of color su. Well known for its accessibility to graduate students and experimental physicists, this volume emphasizes physical arguments and minimizes theoretical formalism. The ginzburglandau theory flux quantization persistent currents the josephson effects. First, ginzburg and landau gl created a theory describing the transition between the superconducting and the normal phases ginzburg and landau, 1950. Find materials for this course in the pages linked along the left. Ginzburglandau vortices, coulomb gases, and abrikosov. In 1950, ginzburg and landau proposed a macroscopic theory of super conductivity based on a variational functional the free energy associated with a complexvalued order parameter and the magnetic vector poten. Vortices in the ginzburglandau model of superconductivity. Lecture notes on superconductivity a work in progress daniel arovas congjun wu department of physics university of california, san diego june 23, 2019. Superconductivity and ginzburg landau theory stefan k. Uniqueness of symmetric vortex solutions in the ginzburg. A clue as to the nature of the order parameter which occurs in the ginzburglandau phenomenology is given by the fact that the behavior of super. Even certain semiconductors can be made superconducting. General free energy functional for a superconductor.
It is written for the fresh reader in superconductivity and can be omitted by readers with a. In ginzburglandau theory the electrons that contribute to superconductivity were proposed to form a superfluid. Perfect conductivity of superconductors was discovered in 1911 kamerlinghonnes perfect diamagnetism of superconductors was discovered in 1932 meissner and ochsenfeld microscopic theory of superconductivity known since 1957 bardeen, cooper, and schrie er macroscopic theories know since 1935 london and london and 1950 ginzburg and landau. In its initial form, it was postulated as a phenomenological model which could describe typei superconductors without examining their microscopic properties. Magnetic flux lines in complex geometry typeii superconductors studied by the time dependent.
Based on a socalled phenomenological order parameter. The ginzburg landau energy is the standard model for superconductivity, able to predict the existence of vortices which are quantized, topological defects in. Solving the ginzburglandau equations by finiteelement. Ginzburglandau equations which give an excellent description of super conductivity near t c, in terms of a complex order parameter, as mentioned by schrieffer in his talk. In the usual ginzburglandau theory, it is r that is taken as the wave function or order parameter, as it is sometimes called in that theory, because, as we shall see, the internal angular part does not matter for symmetry reasons in the case of an in nite sample. Some of the key ideas for the landau mean field description of phase transitions were developed in the context of. It gives a macroscopic description of a superconducting material in terms of a complexvalued order parameter where n. The problem of formulating a microscopic theory of superconductivity is also considered. The authors describe all relevant superconducting phenomena and rely on the macroscopic ginzburglandau theory to derive the most important results.
The second essential observation was that superconductors not only prevent a magnetic. Notes on the ginzburglandau theory international center for. The superconducting properties of small specimens 9. Prior to his studies of superconductivity, landau had developed a simple mean field theory to describe phase transitions. The near critical regime is therefore both interesting and very complicated. In nite conductivity implies that if a current were passed through the material during its. In the modern view, superconductivity is understood as a phase ordering of pairs. Ball abstract we study the dynamics of vortices in timedependent ginzburg. Chapter one superconductivity 4 the supercurrent density is given by. Introduction to superconductivity and hightc materials. Finally, it was in 1950 that fritz londons book 7 on superconductivity appeared. Solving the ginzburglandau equations by finiteelement methods q. Macroscopic theory of superconductivity valid for magnetic fields of arbitrary magnitude and the behaviour of superconductors in weak high frequency fields are discussed.
It can be noted that, when it appeared, the gl theory looked rather phenomenological and was not really appreciated in the. In the usual ginzburg landau theory, it is r that is taken as the wave function or order parameter, as it is sometimes called in that theory, because, as we shall see, the internal angular part does not matter for symmetry reasons in the case of an in nite sample. The time dependent ginzburglandau equation is a phenomenological model for the dy. Vortices in the ginzburg landau model of superconductivity sylvia serfaty abstract. The book discusses the fundamental principles of superconductivity. But i resort to the term theory of superconductivity, because it seems to me that using ones own name rings, at least in russian, somewhat pretentiously. It turns out that for conventional lowtc superconductors, mean. Not strictly an ab initio theory, but essential for problems concerning superconductors in magnetic fields. If the magnetic eld is too large however, then it destroys the super conductivity and penetrates the sample. But until abrikosov and ginzburgs theory, building on work by a previous nobel winner, lev landau, theorists struggled to explain the behaviour of a class of superconductors, called type ii.
It is written for the fresh reader in superconductivity and can be omitted by readers with a very general background in this field. In 1950, the phenomenological ginzburglandau theory of superconductivity was devised by landau and ginzburg. Landau proposed a phenomenological theory for super. Dynamics of vortices in ginzburglandau theories with. Lecture notes applied superconductivity electrical. Ginzburglandau vortices, coulomb gases, and abrikosov lattices sylvia serfaty may 30, 2014. Surface boundary conditions for the ginzburglandau theory. Around 1960 gorkov 10 showed that the phenomenological ginzburg landau theory is a limiting case of the bcs theory. Introduction to superconductivity pdf 26p covered topics are. The rst mathematically rigorous proof that ginzburglandau theory arises from bcs theory, on macroscopic length scales and for temperatures close to t c, was given in 16 under the nondegeneracy assumption that there is only one type of super conductivity present in the system. Introduction superconductivity discovered in 1911 by onnes 9, is the. Free superconductivity books download ebooks online. Lecture notes on superconductivity a work in progress.
A great deal was known about the phenomenology of super conductivity in the 1950s, and it was already suspected that. In this article, an introductory survey gives the main features of super conductivity in connection with the history of the ginzburg landau theory. It is scaled by the factor 1 0d 2, where 0 is the magnetic permeability of the free space. The second edition of this classic text features revisions by the author that improve its userfriendly qualities, and an introductory survey of latterday developments in classic superconductivity enhances the volumes value as a. This book included very perceptive comments about the nature of the microscopic theory. H elsevier physica d 77 1994 383404 dynamics of vortices in ginzburg landau theories with applications to superconductivity weinan e school of mathematics, institute for advanced study, princeton, nj 08540, usa received 20 october 1993. Ginzburglandau theory this is a phenomenological theory, unlike the microscopic bcs theory. Introductionzero resistance, perfect diamagnetism, electrodynamics or the london theory,the critical magnetic field, thermodynamics of the transition, the intermediate state, transport currents in superconductors, the superconducting properties of small specimens, ginzburglandau.
Around 1960 gorkov 10 showed that the phenomenological ginzburglandau theory is. If a current is set up in a super conductor with multiply connected topology, e. In bulk physical systems, the subcritical and super critical cases exhibit distinctly di erent behaviour, in agreement with the predictions of the gl theory. Ginzburglandau theory for superconductors iopscience. We will compare also the electronphonon mechanism for superconductivity with possible alternative mechanisms, in particular, based on effective interaction. Ginzburglandau theory already allows to understand many phenomena. The ginzburglandau theory 9 provides a theoretical basis for the distinction between the two types. In physics, ginzburg landau theory, often called landau ginzburg theory, named after vitaly lazarevich ginzburg and lev landau, is a mathematical physical theory used to describe superconductivity. Superconductivity covers the nature of the phenomenon of superconductivity. For comparison, the resistivity of copper at room temperature is.
The ginzburglandau equations lead to two characteristic lengths, the gl penetration depth. Below tc the lower curve gives the thermal conductivity in. Superconducting materials exhibit the following unusual be haviors. In this article, an introductory survey gives the main features of super conductivity in connection with the history of the ginzburglandau theory. The phenomena include scaling and renormalization effects on specific heat and magnetization near t.
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