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Abrikosov Vortex
In superconductivity, a fluxon (also called an Abrikosov vortex or quantum vortex) is a vortex of supercurrent in a type-II superconductor, used by Soviet physicist Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity. Overview The solution is a combination of fluxon solution by Fritz London, combined with a concept of core of quantum vortex by Lars Onsager. In the quantum vortex, supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size \sim\xi — the superconducting coherence length (parameter of a Ginzburg–Landau theory). The supercurrents decay on the distance about \lambda (London penetration depth) from the core. Note that in type-II superconductors \lambda>\xi/\sqrt. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum \Phi_0. Therefore, an Abrikosov vortex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YBCO Vortices
Yttrium barium copper oxide (YBCO) is a family of crystalline chemical compounds that display high-temperature superconductivity; it includes the first material ever discovered to become superconducting above the boiling point of liquid nitrogen [] at about . Many YBCO compounds have the general formula (also known as Y123), although materials with other Y:Ba:Cu ratios exist, such as (Y124) or (Y247). At present, there is no singularly recognised theory for high-temperature superconductivity. It is part of the more general group of rare-earth barium copper oxides (ReBCO) in which, instead of yttrium, other rare earths are present. History In April 1986, Georg Bednorz and Karl Müller, working at IBM in Zurich, discovered that certain semiconducting oxides became superconducting at relatively high temperature, in particular, a lanthanum barium copper oxide becomes superconducting at 35 K. This oxide was an oxygen-deficient perovskite-related material that proved promis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Penetration Depth
In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface of the superconductor. Typical values of λL range from 50 to 500 nm. It was first derived by Geertruida de Haas-Lorentz in 1925, and later by Fritz and Heinz London in their London equations (1935).Fossheim, Kristian, and Asle Sudbø. ''Superconductivity: physics and applications''. John Wiley & Sons, 2005. The London penetration depth results from considering the London equation and Ampère's circuital law. If one considers a superconducting half-space, i.e. superconducting for x>0, and weak external magnetic field B0 applied along ''z'' direction in the empty space ''x''<0, then inside the superconductor the magnetic field is given by |
Nielsen–Olesen Vortex
In theoretical physics, a Nielsen–Olesen vortex is a point-like object localized in two spatial dimensions or, equivalently, a classical solution of field theory with the same property. This particular solution occurs if the configuration space of scalar fields contains non-contractible circles. A circle surrounding the vortex at infinity may be "wrapped" once on the other circle in the configuration space. A configuration with this non-trivial topological property is called the Nielsen–Olesen vortex, after Holger Bech Nielsen and Poul Olesen (1973). The solution is formally identical to the solution of Quantum vortex in superconductor. See also * Nielsen–Olsen string * Abrikosov vortex *Montonen–Olive duality *S-duality In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theore ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macroscopic Quantum Phenomena
Macroscopic quantum phenomena are processes showing Quantum mechanics, quantum behavior at the macroscopic scale, rather than at the Atom, atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect, Josephson effect and topological order. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein condensates. Between 1996 and 2016 six Nobel Prizes were given for work related to macroscopic quantum phenomena. Macroscopic quantum phenomena can be observed in superfluid helium and in superconductors, but also in dilute quantum gases, dressed particle, dressed photons such as Bose–Einstein condensation of polaritons, polaritons and in laser light. Although these media are very different, they are all similar in that they show macroscopic quantum behavior, and in this respect they all can be referred to as quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper Critical Field
For a given temperature, the critical field refers to the maximum magnetic field strength below which a material remains superconducting. Superconductivity is characterized both by perfect conductivity (zero resistance) and by the complete expulsion of magnetic fields (the Meissner effect). Changes in either temperature or magnetic flux density can cause the phase transition between normal and superconducting states.High Temperature Superconductivity, Jeffrey W. Lynn Editor, Springer-Verlag (1990) The highest temperature under which the superconducting state is seen is known as the critical temperature. At that temperature even the weakest external magnetic field will destroy the superconducting state, so the strength of the critical field is zero. As temperature decreases, the critical field increases generally to a maximum at absolute zero. For a type-I superconductor the discontinuity in heat capacity seen at the superconducting transition is generally related to the slope of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Flux Quantum
The magnetic flux, represented by the symbol , threading some contour or loop is defined as the magnetic field multiplied by the loop area , i.e. . Both and can be arbitrary, meaning that the flux can be as well but increments of flux can be quantized. The wave function can be multivalued as it happens in the Aharonov–Bohm effect or quantized as in superconductors. The unit of quantization is therefore called magnetic flux quantum. Dirac magnetic flux quantum The first to realize the importance of the flux quantum was Dirac in his publication on monopoles The phenomenon of flux quantization was predicted first by Fritz London then within the Aharonov–Bohm effect and later discovered experimentally in superconductors (see ' below). Superconducting magnetic flux quantum If one deals with a superconducting ring (i.e. a closed loop path in a superconductor) or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type-II Superconductors
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of Abrikosov vortex, magnetic field vortices with an applied external magnetic field. This occurs above a certain critical field strength ''Hc1''. The vortex density increases with increasing field strength. At a higher critical field ''Hc2'', superconductivity is destroyed. Type-II superconductors do not exhibit a complete Meissner effect. History In 1935, J.N. Rjabinin and Lev Shubnikov experimentally discovered the type-II superconductors. In 1950, the theory of the two types of superconductors was further developed by Lev Landau and Vitaly Ginzburg in their paper on Ginzburg–Landau theory. In their argument, a type-I superconductor had positive Thermodynamic free energy, free energy of the superconductor-normal metal bounda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconducting Coherence Length
In superconductivity, the superconducting coherence length, usually denoted as \xi (Greek lowercase ''xi''), is the characteristic exponent of the variations of the density of superconducting component. The superconducting coherence length is one of two parameters in the Ginzburg–Landau theory of superconductivity. It is given by: : \xi = \sqrt where \alpha(T) is a parameter in the Ginzburg–Landau theory#Simple interpretation, Ginzburg–Landau equation for \psi with the form \alpha_0 (T-T_c), where \alpha_0 is a constant. In Landau mean-field theory, at temperatures T near the superconducting critical temperature T_c, \xi (T) \propto (1-T/T_c)^. Up to a factor of \sqrt, it is equivalent to the characteristic exponent describing a recovery of the order parameter away from a perturbation in the theory of the second order phase transitions. In some special limiting case (mathematics), limiting cases, for example in the weak-coupling BCS theory of isotropic s-wave superconducto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconductivity
Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ordinary metallic Electrical conductor, conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic Phase transition, critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source. The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and Atomic spectral line, atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect, the complete cancellation of the magnetic field in the interior of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lars Onsager
Lars Onsager (November 27, 1903 – October 5, 1976) was a Norwegian American physical chemist and theoretical physicist. He held the Gibbs Professorship of Theoretical Chemistry at Yale University. He was awarded the Nobel Prize in Chemistry in 1968. Education and early life Lars Onsager was born in Kristiania (now Oslo), Norway. His father was a lawyer. After completing secondary school in Oslo, he attended the Norwegian Institute of Technology, Norwegian Institute of Technology (NTH) in Trondheim, graduating as a chemical engineering, chemical engineer in 1925. While there he worked through ''A Course of Modern Analysis'', which was instrumental in his later work. Career and research In 1925 he arrived at a correction to the Debye–Hückel equation, Debye-Hückel theory of electrolyte, electrolytic Solution (chemistry), solutions, to specify Brownian movement of ions in solution, and during 1926 published it. He traveled to Zürich, where Peter Debye was teaching, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
