It is written for the fresh reader in superconductivity and can be omitted by readers with a. We will compare also the electronphonon mechanism for superconductivity with possible alternative mechanisms, in particular, based on effective interaction. In this article, an introductory survey gives the main features of super conductivity in connection with the history of the ginzburg landau theory. Introduction superconductivity refers to a complex of phenom. Ginzburglandau theory this is a phenomenological theory, unlike the microscopic bcs theory. The time dependent ginzburglandau equation is a phenomenological model for the dy.
In the modern view, superconductivity is understood as a phase ordering of pairs. Introduction superconductivity discovered in 1911 by onnes 9, is the. 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. And it encompasses two rich topics within super conductivity i josephson junctions, and ii the abrikosov vortexlattice phase of.
The second essential observation was that superconductors not only prevent a magnetic. Ginzburglandau theory already allows to understand many phenomena. 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. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. Free superconductivity books download ebooks online. The superconducting properties of small specimens 9. Vortices in the ginzburglandau model of superconductivity. 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. Ginzburglandau vortices, coulomb gases, and abrikosov. Solving the ginzburglandau equations by finiteelement. Not strictly an ab initio theory, but essential for problems concerning superconductors in magnetic fields. Around 1960 gorkov 10 showed that the phenomenological ginzburglandau theory is.
Solving the ginzburglandau equations by finiteelement methods q. If a current is set up in a super conductor with multiply connected topology, e. The ginzburglandau equations lead to two characteristic lengths, the gl penetration depth. Even certain semiconductors can be made superconducting. The book discusses the fundamental principles of superconductivity. Vortices in the ginzburg landau model of superconductivity sylvia serfaty abstract. What sets this book apart from others on the introduction to superconductivity and high t c materials is its simple and pragmatic approach. Lecture notes applied superconductivity electrical. Superconductivity and ginzburg landau theory stefan k. 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.
It turns out that for conventional lowtc superconductors, mean. The phenomena include scaling and renormalization effects on specific heat and magnetization near t. 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. 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. Some of the key ideas for the landau mean field description of phase transitions were developed in the context of. Landau proposed a phenomenological theory for super. Ball abstract we study the dynamics of vortices in timedependent ginzburg. Chapter one superconductivity 4 the supercurrent density is given by. General free energy functional for a superconductor. The ginzburglandau theory flux quantization persistent currents the josephson effects. Around 1960 gorkov 10 showed that the phenomenological ginzburg landau theory is a limiting case of the bcs theory. If the magnetic eld is too large however, then it destroys the super conductivity and penetrates the sample. In physics, ginzburglandau theory, often called landauginzburg theory, named after vitaly.
It can be noted that, when it appeared, the gl theory looked rather phenomenological and was not really appreciated in the. For comparison, the resistivity of copper at room temperature is. Superconductivity covers the nature of the phenomenon of superconductivity. 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. 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. Niicroscopic derivation of the ginzburglandau equations. 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. The near critical regime is therefore both interesting and very complicated.
Find materials for this course in the pages linked along the left. Below tc the lower curve gives the thermal conductivity in. Introduction to superconductivity pdf 26p covered topics are. It gives a macroscopic description of a superconducting material in terms of a complexvalued order parameter where n. More than 20 metallic elements can become super conductors table 34. Mathematical models and numerical simulations of superconductivity. 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. 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. Lecture notes on superconductivity a work in progress daniel arovas congjun wu department of physics university of california, san diego june 23, 2019.
It is written for the fresh reader in superconductivity and can be omitted by readers with a very general background in this field. In this article, an introductory survey gives the main features of super conductivity in connection with the history of the ginzburglandau theory. Ginzburglandau theory some of the key ideas for the landau mean. Based on a socalled phenomenological order parameter. A great deal was known about the phenomenology of super conductivity in the 1950s, and it was already suspected that. In its initial form, it was postulated as a phenomenological model which could describe typei superconductors without examining their microscopic properties. The problem of formulating a microscopic theory of superconductivity is also considered. 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. Well known for its accessibility to graduate students and experimental physicists, this volume emphasizes physical arguments and minimizes theoretical formalism. First, ginzburg and landau gl created a theory describing the transition between the superconducting and the normal phases ginzburg and landau, 1950.
Magnetic flux lines in complex geometry typeii superconductors studied by the time dependent. Superconducting materials exhibit the following unusual be haviors. In 1950, the phenomenological ginzburglandau theory of superconductivity was devised by landau and ginzburg. The ginzburg landau theory 9 provides a theoretical basis for the distinction between the two types. The ginzburg landau energy is the standard model for superconductivity, able to predict the existence of vortices which are quantized, topological defects in. Dynamics of vortices in ginzburglandau theories with.
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. This book included very perceptive comments about the nature of the microscopic theory. Ginzburglandau theory for superconductors iopscience. Macroscopic theory of superconductivity valid for magnetic fields of arbitrary magnitude and the behaviour of superconductors in weak high frequency fields are discussed. In nite conductivity implies that if a current were passed through the material during its. Perfect conductivity below a critical tc, electrical resistance becomes zero infinite conductance. The ginzburglandau theory 9 provides a theoretical basis for the distinction between the two types. Notes on the ginzburglandau theory international center for. Historically, gl theory was an extension of the landau theory of secondorder phase transitions3 onto the quantum phenomenon of superconductivity. Prior to his studies of superconductivity, landau had developed a simple mean field theory to describe phase transitions. Surface boundary conditions for the ginzburglandau theory.
265 404 1129 223 1343 485 1561 365 1598 806 79 899 192 1199 792 536 409 619 1018 1373 1118 747 1183 417 985 496 1094 431 56 541 1299 227 1047 1170 1415 1209