Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic 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.
Superfluid helium-4 is the superfluid form of helium-4, an isotope of the element helium. A superfluid is a state of matter in which matter behaves like a fluid with zero viscosity. The substance, which resembles other liquids such as helium I, flows without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own inertia.
Unconventional superconductors are materials that display superconductivity which is not explained by the usual BCS theory or its extension, the Eliashberg theory. The pairing in unconventional superconductors may originate from some other mechanism than the electron–phonon interaction. Alternatively, a superconductor is unconventional if the superconducting order parameter transforms according to a non-trivial irreducible representation of the point group or space group of the system. Per definition, superconductors that break additional symmetries to U (1) symmetry are known as unconventional superconductors.
In condensed-matter physics, the Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby magnet.
The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary, meaning that the flux Φ 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.
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. One GL-type superconductor is the famous YBCO, and generally all cuprates.
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
Magnesium diboride is the inorganic compound of magnesium and boron with the formula MgB2. It is a dark gray, water-insoluble solid. The compound has attracted attention because it becomes superconducting at 39 K (−234 °C). In terms of its composition, MgB2 differs strikingly from most low-temperature superconductors, which feature mainly transition metals. Its superconducting mechanism is primarily described by BCS theory.
The Berezinskii–Kosterlitz–Thouless (BKT) transition is a phase transition of the two-dimensional (2-D) XY model in statistical physics. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Thouless. BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition.
In superconductivity, a fluxon 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.
In superconductivity, the superconducting coherence length, usually denoted as , is the characteristic exponent of the variations of the density of superconducting component.
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 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.
The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is
The London equations, developed by brothers Fritz and Heinz London in 1935, are constitutive relations for a superconductor relating its superconducting current to electromagnetic fields in and around it. Whereas Ohm's law is the simplest constitutive relation for an ordinary conductor, the London equations are the simplest meaningful description of superconducting phenomena, and form the genesis of almost any modern introductory text on the subject. A major triumph of the equations is their ability to explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold.
In a standard superconductor, described by a complex field fermionic condensate wave function, vortices carry quantized magnetic fields because the condensate wave function is invariant to increments of the phase by . There a winding of the phase by creates a vortex which carries one flux quantum. See quantum vortex.
Ferromagnetic superconductors are materials that display intrinsic coexistence of ferromagnetism and superconductivity. They include UGe2, URhGe, and UCoGe. Evidence of ferromagnetic superconductivity was also reported for ZrZn2 in 2001, but later reports question these findings. These materials exhibit superconductivity in proximity to a magnetic quantum critical point.
Covalent superconductors are superconducting materials where the atoms are linked by covalent bonds. The first such material was boron-doped synthetic diamond grown by the high-pressure high-temperature (HPHT) method. The discovery had no practical importance, but surprised most scientists as superconductivity had not been observed in covalent semiconductors, including diamond and silicon.
Type-1.5 superconductors are multicomponent superconductors characterized by two or more coherence lengths, at least one of which is shorter than the magnetic field penetration length , and at least one of which is longer. This is in contrast to single-component superconductors, where there is only one coherence length and the superconductor is necessarily either type 1 or type 2. When placed in magnetic field, type-1.5 superconductors should form quantum vortices: magnetic-flux-carrying excitations. They allow magnetic field to pass through superconductors due to a vortex-like circulation of superconducting particles. In type-1.5 superconductors these vortices have long-range attractive, short-range repulsive interaction. As a consequence a type-1.5 superconductor in a magnetic field can form a phase separation into domains with expelled magnetic field and clusters of quantum vortices which are bound together by attractive intervortex forces. The domains of the Meissner state retain the two-component superconductivity, while in the vortex clusters one of the superconducting components is suppressed. Thus such materials should allow coexistence of various properties of type-I and type-II superconductors.
In superconductivity, a Pearl vortex is a vortex of supercurrent in a thin film of type-II superconductor, first described in 1964 by Judea Pearl. A Pearl vortex is similar to Abrikosov vortex except for its magnetic field profile which, due to the dominant air-metal interface, diverges sharply as 1/ at short distances from the center, and decays slowly, like 1/ at long distances. Abrikosov's vortices, in comparison, have very short range interaction and diverge as near the center.
