superconductivity

Dictionary: su·per·con·duc·tiv·i·ty (sū'pər-kŏn'dŭk-tĭv'ĭ-tē) pronunciation

n.
The flow of electric current without resistance in certain metals, alloys, and ceramics at temperatures near absolute zero, and in some cases at temperatures hundreds of degrees above absolute zero.

superconductive su'per·con·duc'tive (-kən-dŭk'tĭv) adj.
superconductor su'per·con·duc'tor (-dŭk'tər) n.

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Britannica Concise Encyclopedia: superconductivity

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Almost total lack of electrical resistance in certain materials when they are cooled to a temperature near absolute zero. Superconducting materials allow low power dissipation, high-speed operation, and high sensitivity. They also have the ability to prevent external magnetic fields from penetrating their interiors and are perfect diamagnets (see diamagnetism). Since it was first discovered in mercury by Heike Kamerlingh Onnes in 1911, similar behaviour has been found in some 25 other chemical elements and in thousands of alloys and compounds. Superconductors have applications in medical imaging, magnetic energy-storage systems, motors, generators, transformers, computer components, and sensitive magnetic-field measuring devices.

For more information on superconductivity, visit Britannica.com.

Sci-Tech Encyclopedia: Superconductivity

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A phenomenon occurring in many electrical conductors, in which the electrons responsible for conduction undergo a collective transition into an ordered state with many unique and remarkable properties. These include the vanishing of resistance to the flow of electric current, the appearance of a large diamagnetism and other unusual magnetic effects, substantial alteration of many thermal properties, and the occurrence of quantum effects otherwise observable only at the atomic and subatomic level.

Superconductivity was discovered by H. Kamerlingh Onnes in Leiden in 1911 while studying the temperature dependence of the electrical resistance of mercury within a few degrees of absolute zero. He observed that the resistance dropped sharply to an unmeasurably small value at a temperature of 4.2 K (−452°F). The temperature at which the transition occurs is called the transition or critical temperature, T_c. The vanishingly small resistance (very high conductivity) below T_c suggested the name given the phenomenon.

In 1933 W. Meissner and R. Ochsenfeld discovered that a metal cooled into the superconducting state in a moderate magnetic field expels the field from its interior. This discovery demonstrated that superconductivity involves more than simply very high or infinite electrical conductivity, remarkable as that alone is. See also Meissner effect.

In 1957, J. Bardeen, L. N. Cooper, and J. R. Schrieffer reported the first successful microscopic theory of superconductivity. The Bardeen-Cooper-Schrieffer (BCS) theory describes how the electrons in a conductor form the ordered superconducting state. The BCS theory still stands as the basic explanation of superconductivity, even though extensive theoretical work has embellished it.

There are a number of practical applications of superconductivity. Powerful superconducting electromagnets guide elementary particles in particle accelerators, and they also provide the magnetic field needed for magnetic resonance imaging. Ultrasensitive superconducting circuits are used in medical studies of the human heart and brain and for a wide variety of physical science experiments. A completely superconducting prototype computer has even been built. See also Medical imaging; Particle accelerator; Superconducting devices.

Transition temperatures

It was realized from the start that practical applications of superconductivity could become much more widespread if a high-temperature superconductor, that is, one with a high T_c, could be found. For instance, the only practical way to cool superconductors with transition temperatures below 20 K (−424°F) is to use liquid helium, which boils at a temperature of 4.2 K (−452°F) and which is rather expensive. On the other hand, a superconductor with a transition temperature of 100 K (−280°F) could be cooled with liquid nitrogen, which boils at 77 K (−321°F) and which is roughly 500 times less expensive than liquid helium. Another advantage of a high-T_c material is that, since many of the other superconducting properties are proportional to T_c, such a material would have enhanced properties. In 1986 the discovery of transition temperatures possibly as high as 30 K (−406°F) was reported in a compound containing barium, lanthanum, copper, and oxygen. In 1987 a compound of yttrium, barium, copper, and oxygen was shown to be superconducting above 90 K (−298°F). In 1988 researchers showed that a bismuth, strontium, calcium, copper, and oxygen compound was superconducting below 110 K (−262°F), and transition temperatures as high as 135 K (−216°F) were found in a mercury, thallium, barium, calcium, copper, and oxygen compound.

Occurrence

Some 29 metallic elements are known to be superconductors in their normal form, and another 17 become superconducting under pressure or when prepared in the form of thin films. The number of known superconducting compounds and alloys runs into the thousands. Superconductivity is thus a rather common characteristic of metallic conductors. The phenomenon also spans an extremely large temperature range. Rhodium is the element with the lowest transition temperature (370 μK), while Hg_0.2Tl_0.8Ca₂Ba₂Cu₃O is the compound with the highest (135 K or −216°F).

Despite the existence of a successful microscopic theory of superconductivity, there are no completely reliable rules for predicting whether a metal will be a superconductor. Certain trends and correlations are apparent among the known superconductors, however—some with obvious bases in the theory—and these provide empirical guidelines in the search for new superconductors. Superconductors with relatively high transition temperatures tend to be rather poor conductors in the normal state.

The ordered superconducting state appears to be incompatible with any long-range-ordered magnetic state: Usually the ferromagnetic or antiferromagnetic metals are not superconducting. The presence of nonmagnetic impurities in a superconductor usually has very little effect on the superconductivity, but the presence of impurity atoms which have localized magnetic moments can markedly depress the transition temperature even in concentrations as low as a few parts per million. See also Antiferromagnetism; Ferromagnetism.

Some semiconductors with very high densities of charge carriers are superconducting, and others such as silicon and germanium have high-pressure metallic phases which are superconducting. Many elements which are not themselves superconducting form compounds which are.

Certain organic conductors are superconducting. For instance, brominated polymeric chains of sulfur and nitrogen, known as (SNBr_0.4)_x, are superconducting below 0.36 K. Other more complicated organic materials have T_c values near 10 K (−442°F). See also Organic conductor.

Although nearly all the classes of crystal structure are represented among superconductors, certain structures appear to be especially conducive to high-temperature superconductivity. The so-called A15 structure, shared by a series of intermetallic compounds based on niobium, produced several superconductors with T_c values above 15 K (−433°F) as well as the record holder, NbGe, at 23 K (−418°F). Indeed, the robust applications of superconductivity that depend on the ability to carry high current in the presence of high magnetic fields still exclusively use two members of this class: NbTi with T_c = 8 K (−445°F), and Nb₃Sn with T_c = 18.1 K (−427°F). See also A15 phases.

After 1986 the focus of superconductivity research abruptly shifted to the copper-oxide-based planar structures, due to their significantly higher transition temperatures. Basically there are three classes of these superconductors, all of which share the common feature that they contain one or more conducting planes of copper and oxygen atoms. The first class is designated by the chemical formula La_2−xA_xCuO₄, where the A atom can be barium, strontium, or calcium. Superconductivity was originally discovered in the barium-doped system, and systematic study of the substitutions of strontium, calcium, and so forth have produced transition temperatures as high as 40 K (−388°F).

The second class of copper-oxide superconductor is designated by the chemical formula Y₁Ba₂Cu₃O_7−δ, with δ < 1.0. Here, single sheets of copper and oxygen atoms straddle the rare-earth yttrium ion and chains of copper and oxygen atoms thread among the barium ions. The transition temperature, 92 K (−294°F), is quite insensitive to replacement of yttrium by many other rare-earth ions. See also Rare-earth elements.

The third class is the most complicated. These compounds contain either single thallium-oxygen layers, represented by the chemical formula Tl₁Ca_n−1Ba₂Cu_nO_2n+3, where n refers to the number of copper-oxygen planes, or double thallium-oxygen layers, represented by the chemical formula Tl₂Ca_n−1Ba₂Cu_nO_2n+4. The number of copper-oxygen planes may be varied, and as many as three planes have been included in the structure. Thallium may be replaced by bismuth, thus generating a second family of superconductors. In all of these compounds, the transition temperature appears to increase with the number of planes, but T_c decreases for larger values of n.

The spherical molecule comprising 60 carbon atoms (C₆₀), known as a buckyball, can be alloyed with various alkaline atoms which contribute electrons for conduction. By varying the number of conductors in C₆₀, it is possible to boost T_c to a maximum value of 52 K (−366°F). See also Fullerene.

Superconductivity was discovered in magnesium diboride (MgB₂) in January 2001 in Japan. This material may be a good alternative for some of the applications envisioned for high-T_c superconductivity, since this compound has T_c of 39 K (−389°F), is relatively easy to make, and consists of only two elements.

Magnetic properties

The existence of the Meissner-Ochsenfeld effect, the exclusion of a magnetic field from the interior of a superconductor, is direct evidence that the superconducting state is not simply one of infinite electrical conductivity. Instead, it is a true thermodynamic equilibrium state, a new phase which has lower free energy than the normal state at temperatures below the transition temperature and which somehow requires the absence of magnetic flux.

The exclusion of magnetic flux by a superconductor costs some magnetic energy. So long as this cost is less than the condensation energy gained by going from the normal to the superconducting phase, the superconductor will remain completely superconducting in an applied magnetic field. If the applied field becomes too large, the cost in magnetic energy will outweigh the gain in condensation energy, and the superconductor will become partially or totally normal. The manner in which this occurs depends on the geometry and the material of the superconductor. The geometry which produces the simplest behavior is that of a very long cylinder with field applied parallel to its axis. Two distinct types of behavior may then occur, depending on the type of superconductor—type I or type II.

Below a critical field H_c which increases as the temperature decreases below T_c, the magnetic flux is excluded from a type I superconductor, which is said to be perfectly diamagnetic. For a type II superconductor, there are two critical fields, the lower critical field H_c1 and the upper critical field H_c2. In applied fields less than H_c1, the superconductor completely excludes the field, just as a type I superconductor does below H_c. At fields just above H_c1, however, flux begins to penetrate the superconductor, not in a uniform way, but as individual, isolated microscopic filaments called fluxoids or vortices. Each fluxoid consists of a normal core in which the magnetic field is large, surrounded by a superconducting region in which flows a vortex of persistent supercurrent which maintains the field in the core. See also Diamagnetism.

Thermal properties

The appearance of the superconducting state is accompanied by rather drastic changes in both the thermodynamic equilibrium and thermal transport properties of a superconductor.

The heat capacity of a superconducting material is quite different in the normal and superconducting states. In the normal state (produced at temperatures below the transition temperature by applying a magnetic field greater than the critical field), the heat capacity is determined primarily by the normal electrons (with a small contribution from the thermal vibrations of the crystal lattice) and is nearly proportional to the temperature. In zero applied magnetic field, there appears a discontinuity in the heat capacity at the transition temperature. At temperatures just below the transition temperature, the heat capacity is larger than in the normal state. It decreases more rapidly with decreasing temperature, however, and at temperatures well below the transition temperature varies exponentially as e^−Δ/kT, where Δ is a constant and k is Boltzmann's constant. Such an exponential temperature dependence is a hallmark of a system with a gap Δ in the spectrum of allowed energy states. Heat capacity measurements provided the first indications of such a gap in superconductors, and one of the key features of the macroscopic BCS theory is its prediction of just such a gap.

Ordinarily a large electrical conductivity is accompanied by a large thermal conductivity, as in the case of copper, used in electrical wiring and cooking pans. However, the thermal conductivity of a pure superconductor is less in the superconducting state than in the normal state, and at very low temperatures approaches zero. Crudely speaking, the explanation for the association of infinite electrical conductivity with vanishing thermal conductivity is that the transport of heat requires the transport of disorder (entropy). The superconducting state is one of perfect order (zero entropy), and so there is no disorder to transport and therefore no thermal conductivity. See also Entropy.

Two-fluid model

C. J. Gorter and H. B. G. Casimir introduced in 1934 a phenomenological theory of superconductivity based on the assumption that in the superconducting state there are two components of the conduction electron “fluid” (hence the name given this theory, the two-fluid model). One, called the superfluid component, is an ordered condensed state with zero entropy; hence it is incapable of transporting heat. It does not interact with the background crystal lattice, its imperfections, or the other conduction electron component and exhibits no resistance to flow. The other component, the normal component, is composed of electrons which behave exactly as they do in the normal state. It is further assumed that the superconducting transition is a reversible thermodynamic phase transition between two thermodynamically stable phases, the normal state and the superconducting state, similar to the transition between the liquid and vapor phases of any substance. The validity of this assumption is strongly supported by the existence of the Meissner-Ochsenfeld effect and by other experimental evidence. This assumption permits the application of all the powerful and general machinery of the theory of equilibrium thermodynamics. The results tie together the observed thermodynamic properties of superconductors in a very satisfying way.

Microscopic (BCS) theory

The key to the basic interaction between electrons which gives rise to superconductivity was provided by the isotope effect. It is an interaction mediated by the background crystal lattice and can crudely be pictured as follows: An electron tends to create a slight distortion of the elastic lattice as it moves, because of the Coulomb attraction between the negatively charged electron and the positively charged lattice. If the distortion persists for a brief time (the lattice may ring like a struck bell), a second passing electron will see the distortion and be affected by it. Under certain circumstances, this can give rise to a weak indirect attractive interaction between the two electrons which may more than compensate their Coulomb repulsion.

The first forward step was taken by Cooper in 1956, when he showed that two electrons with an attractive interaction can bind together to form a “bound pair” (often called a Cooper pair) if they are in the presence of a high-density fluid of other electrons, no matter how weak the interaction is. The two partners of a Cooper pair have opposite momenta and spin angular momenta. Then, in 1957, Bardeen, Cooper, and Schrieffer showed how to construct a wave function in which all of the electrons (at least, all of the important ones) are paired. Once this wave function is adjusted to minimize the free energy, it can be used as the basis for a complete microscopic theory of superconductivity.

The successes of the BCS theory and its subsequent elaborations are manifold. One of its key features is the prediction of an energy gap. Excitations called quasiparticles (which are something like normal electrons) can be created out of the superconducting ground state by breaking up pairs, but only at the expense of a minimum energy of Δ per excitation; Δ is called the gap parameter. The original BCS theory predicted that Δ is related to T_c by Δ = 1.76kT_c at T = 0 for all superconductors. This turns out to be nearly true, and where deviations occur they are understood in terms of modifications of the BCS theory. The manifestations of the energy gap in the low-temperature heat capacity and in electromagnetic absorption provide strong confirmation of the theory.

Modern Science: superconductivity

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superconductivity (sooh-puhr-kon-duk-TIV-uh-tee)

A property of some materials in which their electrical resistance drops to zero, and they acquire the ability to carry electric current with no loss of energy whatsoever. Formerly, materials developed superconductivity only at temperatures near absolute zero, but new materials have been found that remain superconductive at temperatures above those of liquid nitrogen. The goal of current research is to find a material that remains superconductive at room temperature.

Computer Desktop Encyclopedia: superconductor

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A material that has little resistance to the flow of electricity. Traditional superconductors operate at absolute zero (-459.67 degrees Fahrenheit or -273.15 degrees Celsius). Experiments in the 1980s raised the temperature to -321 degrees Fahrenheit. By the late 1990s, superconductivity was demonstrated at -164 degrees Fahrenheit.

The major use for superconductors, made of alloys of niobium, is for high-powered magnets in medical imaging machines and particle accelerators. The magnets are cooled with liquid helium or liquid nitrogen. If superconductors can ever be made to work at reasonable temperatures, they will have a dramatic impact on the future of computing as well. In the meantime, the extra cost and bulk required to cool the circuits would make superconductive computers too expensive to commercialize. See Josephson junction.

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Columbia Encyclopedia: superconductivity

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superconductivity, abnormally high electrical conductivity of certain substances. The phenomenon was discovered in 1911 by Kamerlingh Onnes, who found that the resistance of mercury dropped suddenly to zero at a temperature of about 4.2°K. For the next 75 years there followed a rather steady string of announcements of new materials that become superconducting near absolute zero. A major breakthrough occurred in 1986 when Karl Alexander Müller and J. Georg Bednorz announced that they had discovered a new class of copper-oxide materials that become superconducting at temperatures exceeding 70°K. The work of Müller and Bednorz, which earned them the Nobel Prize in Physics in 1987, precipitated a host of discoveries of other high-temperature superconductors that exhibit lossless electrical flow at temperatures up to 125°K.

Classical superconductivity (superconductivity at temperatures near absolute zero) is displayed by some metals, including zinc, magnesium, lead, gray tin, aluminum, mercury, and cadmium. Other metals, such as molybdenum, may exhibit superconductivity after high purification. More than 50 elements are superconductive at temperatures near absolute; some, such as europium, only under extreme pressure as well. Alloys (e.g., two parts of gold to one part of bismuth) and such compounds as tungsten carbide and lead sulfide may also be superconductors.

Thin films of normal metals and superconductors that are brought into contact can form superconductive electronic devices, which replace transistors in some applications. An interesting aspect of the phenomenon is the continued flow of current in a superconducting circuit after the source of current has been shut off; for example, if a lead ring is immersed in liquid helium, an electric current that is induced magnetically will continue to flow after the removal of the magnetic field. Powerful electromagnets, which, once energized, retain magnetism virtually indefinitely, have been developed using several superconductors.

The 1972 Nobel Prize in Physics was awarded to J. Bardeen, L. Cooper, and S. Schrieffer for their theory (known as the BCS theory) of classical superconductors. This quantum-mechanical theory proposes that at very low temperatures electrons in an electric current move in pairs. Such pairing enables them to move through a crystal lattice without having their motion disrupted by collisions with the lattice. Several theories of high-temperature superconductors have been proposed, but none has been experimentally confirmed.

Bibliography

See J. W. Lynn, ed., High-Temperature Superconductivity (1990).

Science Q&A: What is superconductivity?

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Superconductivity is a condition in which many metals, alloys, organic compounds, and ceramics conduct electricity without resistance, usually at low temperatures. Heinke Kamerlingh Omnes, a Dutch physicist, discovered superconductivity in 1911. The modern theory regarding the phenomenon was developed by three American physicists-John Bardeen, Leon N. Cooper, and John Robert Schrieffer. Known as the BCS theory after the three scientists, it postulates that superconductivity occurs in certain materials because the electrons in them, rather than remaining free to collide with imperfections and scatter, form pairs that can flow easily around imperfections and do not lose their energy. Bardeen, Cooper, and Schrieffer received the Nobel Prize in Physics for their work in 1972. A further breakthrough in superconductivity was made in 1986 by J. Georg Bednorz and K. Alex Müller. Bednorz and Müller discovered a ceramic material consisting of lanthanum, barium, copper and oxygen which became superconductive at 35 K (-238°C)-much higher than any other material. Bednorz and Müller won the Nobel Prize in Physics in 1987. This was a significant accomplishment since in most situations the Nobel Prize is awarded for discoveries made as many as 20 to 40 years earlier.

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Science Dictionary: superconductivity

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(sooh-puhr-kon-duk-tiv-uh-tee)

A property of materials by which their electrical resistance goes to zero, and they acquire the ability to carry electric current with no losses whatsoever.

Formerly, materials showed superconductivity only near absolute zero, but new materials have been found that are superconducting at much higher temperatures.

Wikipedia: Superconductivity

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A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (the Meissner effect). This current effectively forms an electromagnet that repels the magnet.

Superconductivity occurs in certain materials at very low temperatures. When superconductive, a material has an electrical resistance of exactly zero and no interior magnetic field (the Meissner effect). It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It cannot be understood simply as the idealization of "perfect conductivity" in classical physics.

The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of copper shows some resistance. In a superconductor however, despite these imperfections, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing in a loop of superconducting wire can persist indefinitely with no power source.^[1]

Superconductivity occurs in many materials: simple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in pure samples of ferromagnetic metals.

In 1986, it was discovered that some cuprate-perovskite ceramic materials have critical temperatures of more than 90 kelvin. These high-temperature superconductors renewed interest in the topic because the current theory could not explain them. From a practical perspective, 90 kelvin is easy to reach with the readily available liquid nitrogen (boiling point 77 kelvin). This means more experimentation and more commercial applications are feasible, especially if materials with even higher critical temperatures could be discovered.

See also the history of superconductivity.

1 Elementary properties of superconductors
2 Theories of superconductivity
3 History of superconductivity
- 3.1 High temperature superconductivity
4 Classification
5 Applications
6 See also
7 Notes
8 References
9 External links

Elementary properties of superconductors

Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, and critical current density at which superconductivity is destroyed.

On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possesses certain distinguishing properties which are largely independent of microscopic details.

Zero electrical "dc" resistance

Electric cables for accelerators at CERN: top, regular cables for LEP; bottom, superconducting cables for the LHC.

The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V/I. If the voltage is zero, this means that the resistance is zero and that the sample is in the superconducting state.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature. Thus, a superconductor does not have exactly zero resistance, however, the resistance is negligibly small.^[1]

In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions. As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance.

The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice, given by kT, where k is Boltzmann's constant and T is the temperature, the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation.

In a class of superconductors known as Type II superconductors, including all known high-temperature superconductors, an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electrical current is applied in conjunction with a strong magnetic field, which may be caused by the electrical current. This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.

Superconducting phase transition

Behavior of heat capacity (c_v, blue) and resistivity (ρ, green) at the superconducting phase transition

In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature T_c. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2009^[update], the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB₂),^[2]^[3] although this material displays enough exotic properties that there is some doubt about classifying it as a "conventional" superconductor.^[4] Cuprate superconductors can have much higher critical temperatures: YBa₂Cu₃O₇, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown. Electron pairing due to phonon exchanges explains superconductivity in conventional superconductors, but it does not explain superconductivity in the newer superconductors that have a very high critical temperature.

Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field. This is because the Gibbs free energy of the superconducting phase increases quadratically with the magnetic field while the free energy of the normal phase is roughly independent of the magnetic field. If the material superconducts in the absence of a field, then the superconducting phase free energy is lower than that of the normal phase and so for some finite value of the magnetic field (proportional to the square root of the difference of the free energies at zero magnetic field) the two free energies will be equal and a phase transition to the normal phase will occur. More generally, a higher temperature and a stronger magnetic field lead to a smaller fraction of the electrons in the superconducting band and consequently a longer London penetration depth of external magnetic fields and currents. The penetration depth becomes infinite at the phase transition.

The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as e^{−α /T} for some constant α. This exponential behavior is one of the pieces of evidence for the existence of the energy gap.

The order of the superconducting phase transition was long a matter of debate. Experiments indicate that the transition is second-order, meaning there is no latent heat. However in the presence of an external magnetic field there is latent heat, as a result of the fact that the superconducting phase has a lower entropy below the critical temperature than the normal phase. It has been experimentally demonstrated ^[5] that, as a consequence, when the magnetic field is increased beyond the critical field, the resulting phase transition leads to a decrease in the temperature of the superconducting material.

Calculations in the 1970s suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field. In the 1980s it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order (i.e., latent heat) within the type I regime, and that the two regions are separated by a tricritical point.^[6] The results were confirmed by Monte Carlo computer simulations.^[7]

Meissner effect

Main article: Meissner effect

When a superconductor is placed in a weak external magnetic field H, the field penetrates the superconductor only a small distance λ, called the London penetration depth, decaying exponentially to zero within the bulk of the material. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100 nm.

The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.

The Meissner effect is distinct from this because a superconductor expels all magnetic fields, not just those that are changing. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.

The Meissner effect was explained by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided

$\nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\,$

where H is the magnetic field and λ is the London penetration depth.

This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.

The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H_c. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H_c1 leads to a mixed state in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength H_c2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors, except niobium, technetium, vanadium and carbon nanotubes, are Type I, while almost all impure and compound superconductors are Type II.

London moment

Conversely, a spinning superconductor generates a magnetic field, precisely aligned with the spin axis. The effect, the London moment, was put to good use in Gravity Probe B. This experiment measured the magnetic fields of four superconducting gyroscopes to determine their spin axes. This was critical to the experiment since it is one of the few ways to accurately determine the spin axis of an otherwise featureless sphere.

Theories of superconductivity

Since discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957).^[8]^[9] Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity, because they fall into the Lambda transition universality class, but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial. The four-dimensional extension of the Ginzburg-Landau theory, the Coleman-Weinberg model, is important in quantum field theory and cosmology.

History of superconductivity

Main article: History of superconductivity

Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared.^[10] In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.

The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect.^[11] In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.^[12]

In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg.^[13] This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had received the 1962 Nobel Prize for other work, and died in 1968).

Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element.^[14]^[15] This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer.^[9] Independently, the superconductivity phenomenon was explained by Nikolay Bogolyubov. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972.

The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian.^[16] In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.^[17]

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse, allowing the construction of the first practical superconducting magnets. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator.^[18] This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum $\Phi_0 = \frac{h}{2e}$ , and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973.

In 2008 it was discovered by Valerii Vinokur and Tatyana Baturina that the same mechanism that produces superconductivity could produce a superinsulator state in some materials, with almost infinite electrical resistance.^[19]

High temperature superconductivity

Main article: High-temperature superconductivity

Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987).^[20] It was shortly found that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K)^[21]. This is important commercially because liquid nitrogen can be produced cheaply on-site from air, and is not prone to some of the problems (for instance solid air plugs) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.

From about 1993, the highest temperature superconductor was a ceramic material consisting of thallium, mercury, copper, barium, calcium, and oxygen (HgBa₂Ca₂Cu₃O_8+δ) with T_c=138 K.^[22]

In February 2008, an iron-based family of high temperature superconductors was discovered.^[23]^[24] Hideo Hosono, of the Tokyo Institute of Technology, and colleagues found lanthanum oxygen fluorine iron arsenide (LaO_1-xF_xFeAs), an oxypnictide that superconducts below 26 K. Replacing the lanthanum in LaO_1-xF_xFeAs with samarium leads to superconductors that work at 55 K.^[25]

Classification

Main article: Superconductor classification

There is not just one criterion to classify superconductors. The most common are:

By their physical properties: they can be Type I (if their phase transition is of first order) or Type II (if their phase transition is of second order).
By the theory to explain them: they can be conventional (if they are explained by the BCS theory or its derivatives) or unconventional (if not).
By their critical temperature: they can be high temperature (generally considered if they reach the superconducting state just cooling them with liquid nitrogen, that is, if T_c > 77 K), or low temperature (generally if they need other techniques to be cooled under their critical temperature).
By material: they can be chemical elements (as mercury or lead), alloys (as niobium-titanium or germanium-niobium), ceramics (as YBCO or the magnesium diboride), or organic superconductors (as fullerenes or carbon nanotubes, which technically might be included between the chemical elements as they are made of carbon).

Applications

Main article: Technological applications of superconductivity

Video of superconducting levitation of YBCO

Superconducting magnets are some of the most powerful electromagnets known. They are used in MRI and NMR machines, mass spectrometers, and the beam-steering magnets used in particle accelerators. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries.

Superconductors have also been used to make digital circuits (e.g. based on the rapid single flux quantum technology) and RF and microwave filters for mobile phone base stations.

Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. SQUIDs are used in scanning SQUID microscopes. Series of Josephson devices are used to define the SI volt. Depending on the particular mode of operation, a Josephson junction can be used as a photon detector or as a mixer. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter photon detectors.

Other early markets are arising where the relative efficiency, size and weight advantages of devices based on high-temperature superconductivity outweigh the additional costs involved.

Promising future applications include high-performance smart grid electric power transmission, transformers, power storage devices, electric motors (e.g. for vehicle propulsion, as in vactrains or maglev trains), magnetic levitation devices, fault current limiters, nanoscopic materials such as buckyballs, nanotubes, composite materials, and superconducting magnetic refrigeration. However, superconductivity is sensitive to moving magnetic fields so applications that use alternating current (e.g. transformers) will be more difficult to develop than those that rely upon direct current.

Finding a cost effective room-temperature superconductor has been an elusive dream of superconductivity research scientists for generations. If such materials could be developed in the future, they might revolutionize our understanding and use of nearly everything that is electric.

Notes

^ ^a ^b John C. Gallop (1990). SQUIDS, the Josephson Effects and Superconducting Electronics. CRC Press. p. 20. ISBN 0750300515.
^ doi:10.1038/3506503
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^ Preuss, Paul (2002-08-14). "A most unusual superconductor and how it works: first-principles calculation explains the strange behavior of magnesium diboride". Research News (Lawrence Berkeley National Laboratory). http://www.lbl.gov/Science-Articles/Archive/MSD-superconductor-Cohen-Louie.html. Retrieved 2009-10-28.
^ Johnston, Hamish (2009-02-17). "Type-1.5 superconductor shows its stripes". Physics World (Institute of Physics). http://physicsworld.com/cws/article/news/37806. Retrieved 2009-10-28.
^ R.L. Dolecek (1954). "Adiabatic Magnetization of a Superconducting Sphere". Phys.Rev. 96: 25–28. doi:10.1103/PhysRev.96.25.
^ H. Kleinert (1982). "Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition". Lett. Nuovo Cimento 35: 405–412. doi:10.1007/BF02754760. http://www.physik.fu-berlin.de/~kleinert/97/97.pdf.
^ J. Hove,S. Mo, A. Sudbo (2002). "Vortex interactions and thermally induced crossover from type-I to type-II superconductivity". Phys. Rev. B 66: 064524. doi:10.1103/PhysRevB.66.064524. http://www.physik.fu-berlin.de/~kleinert/papers/sudbotre064524.pdf.
^ J. Bardeen, L.N. Cooper, and J.R. Schrieffer (1957). "Microscopic Theory of Superconductivity". Phys. Rev. 106 (1): 162–164. doi:10.1103/PhysRev.106.162. http://prola.aps.org/abstract/PR/v106/i1/p162_1.
^ ^a ^b J. Bardeen, L.N. Cooper, and J.R. Schrieffer (1957). "Theory of Superconductivity". Phys. Rev. 108 (5): 1175–1205. doi:10.1103/PhysRev.108.1175. http://link.aps.org/abstract/PR/v108/p1175.
^ H.K. Onnes (1911). "The resistance of pure mercury at helium temperatures". Commun. Phys. Lab. Univ. Leiden 12: 120.
^ W. Meissner and R. Ochsenfeld (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Naturwiss. 21 (44): 787–788. doi:10.1007/BF01504252.
^ F. London and H. London (1935). "The Electromagnetic Equations of the Supraconductor". Proc. R. Soc. London A 149 (866): 71–88. doi:10.1098/rspa.1935.0048. http://links.jstor.org/sici?sici=0080-4630%2819350301%29149%3A866%3C71%3ATEEOTS%3E2.0.CO%3B2-2.
^ V.L. Ginzburg and L.D. Landau (1950). "On the theory of superconductivity". Zh. Eksp. Teor. Fiz. 20 (1064).
^ E.Maxwell (1950). "Isotope Effect in the Superconductivity of Mercury". Phys. Rev. 78 (4): 477. doi:10.1103/PhysRev.78.477. http://link.aps.org/abstract/PR/v78/p477.
^ C. A. Reynolds, B. Serin, W. H. Wright, and L. B. Nesbitt (1950). "Superconductivity of Isotopes of Mercury". Phys. Rev. 78 (4): 487. doi:10.1103/PhysRev.78.487. http://link.aps.org/abstract/PR/v78/p487.
^ N.N. Bogoliubov (1958). "A new method in the theory of superconductivity". Zh. Eksp. Teor. Fiz. 34 (58).
^ L.P. Gor'kov (1959). "Microscopic derivation of the Ginzburg--Landau equations in the theory of superconductivity". Zh. Eksp. Teor. Fiz. 36 (1364).
^ B.D. Josephson (1962). "Possible new effects in superconductive tunnelling". Phys. Lett. 1 (7): 251–253. doi:10.1016/0031-9163(62)91369-0.
^ "Newly discovered fundamental state of matter, a superinsulator, has been created.". Science Daily. April 9, 2008. http://www.sciencedaily.com/releases/2008/04/080408160614.htm. Retrieved 2008-10-23.
^ J.G. Bednorz and K.A. Mueller (1986). "Possible high T_C superconductivity in the Ba-La-Cu-O system". Z. Phys. B64 (2): 189–193. doi:10.1007/BF01303701.
^ M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu (1987). "Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure". Physical Review Letters 58: 908–910. doi:10.1103/PhysRevLett.58.908+.
^ P. Dai, B. C. Chakoumakos, G. F. Sun, K. W. Wong, Y. Xin and D. F. Lu (1995). "Synthesis and neutron powder diffraction study of the superconductor HgBa₂Ca₂Cu₃O_8+δ by Tl substitution". Physica C:Superconductivity 243 (3-4): 201–206. doi:10.1016/0921-4534(94)02461-8.
^ Hiroki Takahashi, Kazumi Igawa, Kazunobu Arii, Yoichi Kamihara, Masahiro Hirano, Hideo Hosono (2008). "Superconductivity at 43 K in an iron-based layered compound LaO_1-xF_xFeAs". Nature 453: 376–378. doi:10.1038/nature06972.
^ Adrian Cho. "Second Family of High-Temperature Superconductors Discovered". ScienceNOW Daily News. http://sciencenow.sciencemag.org/cgi/content/full/2008/417/1.
^ Ren, Zhi-An (2008). ""Superconductivity and phase diagram in iron-based arsenic-oxides ReFeAsO1-d (Re = rare-earth metal) without fluorine doping". EPL (Europhysics Letters) 83: 17002. doi:10.1209/0295-5075/83/17002.

References

Kleinert, Hagen, Gauge Fields in Condensed Matter, Vol. I, "Superflow and vortex lines"; pp. 1—742, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (also readable online: Vol. I)
Anatoly Larkin; Varlamov, Andrei, Theory of Fluctuations in Superconductors, Oxford University Press, Oxford, United Kingdom, 2005 (ISBN 0198528159)
A.G. Lebed (Ed.) (2008). The Physics of Organic Superconductors and Conductors (1^nd ed.). Springer Series in Materials Science , Vol. 110. ISBN 978-3-540-76667-4.
Matricon, Jean; Waysand, Georges; Glashausser, Charles; The Cold Wars: A History of Superconductivity, Rutgers University Press, 2003, ISBN 0813532957
ScienceDaily: Physicist Discovers Exotic Superconductivity (University of Arizona) August 17, 2006
Tinkham, Michael (2004). Introduction to Superconductivity (2^nd ed.). Dover Books on Physics. ISBN 0-486-43503-2 (Paperback).
Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4^th ed.). W. H. Freeman. ISBN 0-7167-4345-0.

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Translations: Superconductive

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Dansk (Danish)
adj. - superledende

Français (French)
adj. - supraconducteur

Deutsch (German)
adj. - supraleitfähig

Ελληνική (Greek)
adj. - υπεραγώγιμος

Italiano (Italian)
superconduttivo

Português (Portuguese)
adj. - supercondutor

Русский (Russian)
сверхпроводимый

Español (Spanish)
adj. - superconductor

Svenska (Swedish)
adj. - supraledande

中文（简体）(Chinese (Simplified))
超传导现象的, 超电导的

中文（繁體）(Chinese (Traditional))
adj. - 超傳導現象的, 超電導的

한국어 (Korean)
adj. - 초전도의

日本語 (Japanese)
adj. - 超伝導を示す

עברית (Hebrew)
adj. - ‮בעל מוליכות-על‬

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