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[[File:Meissner effect p1390048.jpg|thumb|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 ([[Faraday's law of induction]]). This current effectively forms an electromagnet that repels the magnet.]]
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[[File:Meissner effect.ogv|thumb|Video of a Meissner effect in a high temperature superconductor (black pellet) with a NdFeB magnet (metallic)]]
[[File:Stickstoff gekühlter Supraleiter schwebt über Dauermagneten 2009-06-21.jpg|thumb|A high-temperature superconductor levitating above a magnet]]
 
'''Superconductivity''' is a phenomenon of exactly zero [[Electrical resistance and conductance|electrical resistance]] and expulsion of [[magnetic field]]s occurring in certain materials when [[:wikt:cooling|cooled]] below a characteristic [[Phase transition|critical temperature]]. It was discovered by Dutch physicist [[Heike Kamerlingh Onnes]] on April&nbsp;8, 1911 in [[Leiden]]. Like [[ferromagnetism]] and [[atomic spectral line]]s, superconductivity is a [[quantum mechanics|quantum mechanical]] phenomenon. It is characterized by the [[Meissner effect]], the complete ejection of [[magnetic field|magnetic field lines]] from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of ''[[perfect conductor|perfect conductivity]]'' in [[classical physics]].
 
==Explanation==
The electrical resistivity of a metallic [[electrical conductor|conductor]] decreases gradually as temperature is lowered and at the same time its conductivity becomes infinite. Thus a current in a superconductor flows without any change in magnitude. In ordinary [[Electrical conductor|conductors]], such as [[copper]] or [[silver]], this decrease is limited by impurities and other defects. Even near [[absolute zero]], a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An [[electric current]] flowing through a loop of [[superconducting wire]] can persist indefinitely with no power source.<ref name="Gallop">
{{cite book
|author=John C. Gallop
|year=1990
|title=SQUIDS, the Josephson Effects and Superconducting Electronics
|url=http://books.google.com/?id=ad8_JsfCdKQC&printsec=frontcover
|publisher=[[CRC Press]]
|pages=3, 20
|isbn=0-7503-0051-5
}}</ref>
 
In 1986, it was discovered that some [[cuprate]]-[[perovskite (structure)|perovskite]] [[ceramic]] materials have a critical temperature above {{convert|90|K|°C|abbr=on|0}}.<ref name=Bednorz>{{cite journal
| author = J. G. Bednorz and K. A. Müller
| title = Possible high T<sub>c</sub> superconductivity in the Ba−La−Cu−O system
| journal = Z. Physik, B
| volume = 64
| year = 1986
| pages = 189–193
| doi = 10.1007/BF01303701
| issue = 1|bibcode = 1986ZPhyB..64..189B }}</ref> Such a high transition temperature is theoretically impossible for a [[conventional superconductor]], leading the materials to be termed [[high-temperature superconductors]]. [[Liquid nitrogen]] boils at 77&nbsp;K, and superconduction at higher temperatures than this facilitates many experiments and applications that are less practical at lower temperatures. In conventional superconductors, electrons are held together in [[Cooper pair]]s by an attraction mediated by lattice [[phonon]]s. The best available model of high-temperature superconductivity is still somewhat crude. There are currently two main hypotheses – the [[Resonating valence bond theory|resonating-valence-bond theory]], and spin fluctuation which has the most support in the research community.<ref>{{cite journal |title= High-temperature superconductivity at 25: Still in suspense |author=Adam Mann |journal=Nature |date=Jul 20, 2011 |volume=475 |issue=7356 |pages=280–2 |doi=10.1038/475280a |pmid= 21776057 |bibcode = 2011Natur.475..280M }}</ref> The second hypothesis proposed that electron pairing in high-temperature superconductors is mediated by short-range spin waves known as paramagnons.<ref>{{Citation
| last = Pines
| first = D.
| contribution = The Spin Fluctuation Model for High Temperature Superconductivity: Progress and Prospects
| year = 2002
| title = The Gap Symmetry and Fluctuations in High-Tc Superconductors
| pages = 111–142
| place = New York
| publisher = Kluwer Academic
| isbn = 0-306-45934-5
| doi = 10.1007/0-306-47081-0_7}}</ref><ref>{{cite journal |author= P. Monthoux, A. V. Balatsky, and D. Pines  |title= Toward a theory of high-temperature superconductivity in the antiferromagnetically correlated cuprate oxides |journal= Phys. Rev. Lett. |volume=67 |pages= 3448–3451 |year =1991 |doi=10.1103/PhysRevLett.67.3448 |bibcode=1991PhRvL..67.3448M}}</ref>
 
==Classification==
{{Main|Superconductor classification}}
There are many criteria by which superconductors are classified. The most common are:
*'''Response to a magnetic field''': A superconductor can be ''[[Type I superconductor|Type&nbsp;I]]'', meaning it has a single critical field, above which all superconductivity is lost; or ''[[Type II superconductor|Type&nbsp;II]]'', meaning it has two critical fields, between which it allows partial penetration of the magnetic field.
*'''By theory of operation''': It is ''[[conventional superconductor|conventional]]'' if it can be explained by the [[BCS theory]] or its derivatives, or ''[[unconventional superconductor|unconventional]]'', otherwise.
*'''By [[critical temperature]]''': A superconductor is generally considered ''[[high temperature superconductivity|high temperature]]'' if it reaches a superconducting state when cooled using [[liquid nitrogen]] &ndash; that is, at only ''T<sub>c</sub>''&nbsp;> 77&nbsp;K) &ndash; or ''low temperature'' if more aggressive cooling techniques are required to reach its critical temperature.
*'''By material''': Superconductor material classes include [[chemical element]]s (e.g. [[mercury (element)|mercury]] or [[lead]]), [[alloy]]s (such as [[niobium-titanium]], [[germanium-niobium]], and [[niobium nitride]]), [[ceramic]]s ([[YBCO]] and [[magnesium diboride]]), or [[organic superconductor]]s ([[fullerene]]s and [[carbon nanotube]]s; though perhaps these examples should be included among the chemical elements, as they are composed entirely of [[carbon]]).
 
==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 or if the applied field does not exceed a critical value. The existence of these "universal" properties implies that superconductivity is a [[phase (matter)|thermodynamic phase]], and thus possesses certain distinguishing properties which are largely independent of microscopic details.
 
===Zero electrical DC resistance===
[[File:CERN-cables-p1030764.jpg|thumb|Electric cables for accelerators at [[CERN]]. Both the massive and slim cables are rated for 12,500 [[amperes|A]]. ''Top:'' conventional cables for [[LEP]]; ''bottom:'' superconductor-based cables for the [[Large Hadron Collider|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&nbsp;=&nbsp;V&nbsp;/&nbsp;I''. If the voltage is zero, this means that the resistance is zero.
 
Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in [[Superconducting magnet|superconducting electromagnet]]s such as those found in [[magnetic resonance imaging|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.<ref name="Gallop"/>
 
In a normal conductor, an electric current may be visualized as a fluid of [[electron]]s moving across a heavy [[ion]]ic 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 pair]]s. This pairing is caused by an attractive force between electrons from the exchange of [[phonon]]s. Due to [[quantum mechanics]], the [[energy spectrum]] of this Cooper pair fluid possesses an ''[[energy gap]]'', meaning there is a minimum amount of energy Δ''E'' that must be supplied in order to excite the fluid. Therefore, if Δ''E'' 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 superconductor]]s, including all known [[high-temperature superconductor]]s, an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electric current is applied in conjunction with a strong magnetic field, which may be caused by the electric current. This is due to the motion of [[Abrikosov vortex|magnetic 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 {{anchor|Superconducting phase transition}}===
[[File:Cvandrhovst.png|thumb|400px|Behavior of heat capacity (c<sub>v</sub>, 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<sub>c</sub>''. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20&nbsp;[[Kelvin|K]] to less than 1&nbsp;K. Solid [[mercury (element)|mercury]], for example, has a critical temperature of 4.2&nbsp;K. {{As of|2009}}, the highest critical temperature found for a conventional superconductor is 39 K for [[magnesium diboride]] (MgB<sub>2</sub>),<ref>
{{cite journal
|author = Jun Nagamatsu, Norimasa Nakagawa, Takahiro Muranaka, Yuji Zenitani and Jun Akimitsu
|year = 2001
|title = Superconductivity at 39 K in magnesium diboride
|journal = [[Nature (journal)|Nature]]
|volume = 410 |issue = 6824 |page = 63
|doi = 10.1038/35065039
|pmid = 11242039
|bibcode = 2001Natur.410...63N }}</ref><ref>
{{cite news
|author=Paul Preuss
|date=14 August 2002
|title=A most unusual superconductor and how it works: first-principles calculation explains the strange behavior of magnesium diboride
|url =http://www.lbl.gov/Science-Articles/Archive/MSD-superconductor-Cohen-Louie.html
|work =Research News
|publisher=[[Lawrence Berkeley National Laboratory]]
|accessdate = 2009-10-28
}}</ref> although this material displays enough exotic properties that there is some doubt about classifying it as a "conventional" superconductor.<ref>
{{cite news
|author=Hamish Johnston
|date=17 February 2009
|title=Type-1.5 superconductor shows its stripes
|url =http://physicsworld.com/cws/article/news/37806
|work =[[Physics World]]
|publisher=[[Institute of Physics]]
|accessdate = 2009-10-28
}}</ref> [[Cuprate]] superconductors can have much higher critical temperatures: [[YBCO|YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub>]], one of the first cuprate superconductors to be discovered, has a critical temperature of 92&nbsp;K, and mercury-based cuprates have been found with critical temperatures in excess of 130&nbsp;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''<sup>−α/''T''</sup> for some constant, α. This exponential behavior is one of the pieces of evidence for the existence of the [[energy gap]].
 
The [[Second-order transition|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, because the superconducting phase has a lower entropy below the critical temperature than the normal phase. It has been experimentally demonstrated<ref>
{{cite journal
|author = R. L. Dolecek
|year = 1954
|title = Adiabatic Magnetization of a Superconducting Sphere
|journal = [[Physical Review]]
|volume = 96 |issue = 1 |pages = 25–28
|doi = 10.1103/PhysRev.96.25
|bibcode = 1954PhRv...96...25D }}</ref> 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|disorder field theory]], in which the [[vortex line]]s of the superconductor play a major role, that the transition is of second order within the [[Type II superconductor|type II]] regime and of first order (i.e., [[latent heat]]) within the [[Type I superconductor|type I]] regime, and that the two regions are separated by a [[tricritical point]].<ref>
{{cite journal
| author = H. Kleinert
| year = 1982
| title = Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition
| url = http://www.physik.fu-berlin.de/~kleinert/97/97.pdf
| journal = [[Lettere al Nuovo Cimento]]
| volume = 35 | pages = 405–412
| doi = 10.1007/BF02754760
| issue = 13
}}</ref> The results were strongly supported by Monte Carlo computer simulations.<ref>
{{cite journal
| author = J. Hove, S. Mo, A. Sudbo
| year = 2002
| title = Vortex interactions and thermally induced crossover from type-I to type-II superconductivity
| url = http://www.physik.fu-berlin.de/~kleinert/papers/sudbotre064524.pdf
| journal = [[Physical Review B]]
| volume = 66 | page = 064524
| doi = 10.1103/PhysRevB.66.064524
| issue = 6
|arxiv = cond-mat/0202215 |bibcode = 2002PhRvB..66f4524H }}</ref>
 
===Meissner effect===
{{Main|Meissner effect}}
When a superconductor is placed in a weak external [[magnetic field]] '''H''', and cooled below its transition temperature, the magnetic field is ejected. The Meissner effect does not cause the field to be completely ejected but instead the field penetrates the superconductor but only to a very small distance, characterized by a parameter&nbsp;''λ'', called the [[London penetration depth]], decaying exponentially to zero within the bulk of the material. The [[Meissner effect]] is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100&nbsp;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 electric 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—it is the spontaneous expulsion which occurs during transition to superconductivity. 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 given a phenomenological explanation by the brothers [[Fritz London|Fritz]] and [[Heinz London]], who showed that the electromagnetic [[thermodynamic free energy|free energy]] in a superconductor is minimized provided
 
:<math> \nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\, </math>
 
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 [[exponential decay|decays exponentially]] from whatever value it possesses at the surface.
 
A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state 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 superconductor]]s, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value ''H<sub>c</sub>''. Depending on the geometry of the sample, one may obtain an intermediate state<ref>
{{cite book
|author=Lev D. Landau, Evgeny M. Lifschitz
|title=Electrodynamics of Continuous Media
|series=[[Course of Theoretical Physics]]
|volume=8
|publisher=Butterworth-Heinemann
|location=Oxford
|year=1984
|isbn=0-7506-2634-8
}}</ref> consisting of a baroque pattern<ref>
{{cite journal
|author=David J. E. Callaway
|year=1990
|title=On the remarkable structure of the superconducting intermediate state
|journal = [[Nuclear Physics B]]
|volume=344 |pages=627–645
|doi=10.1016/0550-3213(90)90672-Z
|issue=3
|bibcode = 1990NuPhB.344..627C }}</ref> of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In [[Type II superconductor]]s, raising the applied field past a critical value ''H''<sub>''c''1</sub> leads to a mixed state (also known as the vortex state) in which an increasing amount of [[magnetic flux]] penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength ''H''<sub>''c''2</sub>, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called [[fluxon]]s because the flux carried by these vortices is [[quantum|quantized]]. Most pure [[chemical element|elemental]] superconductors, except [[niobium]] and [[carbon nanotube]]s, are Type&nbsp;I, while almost all impure and compound superconductors are Type&nbsp;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|Gravity Probe&nbsp;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.
 
{{anchor|Theories of superconductivity}}
 
==History of superconductivity==
[[File:Ehrenfest Lorentz Bohr Kamerlingh Onnes.jpg|thumb|Heike Kamerlingh Onnes (right), the discoverer of superconductivity]]
{{Main|History of superconductivity}}
 
Superconductivity was discovered on April 8, 1911 by [[Heike Kamerlingh Onnes]], who was studying the resistance of solid [[mercury (element)|mercury]] at [[cryogenic]] temperatures using the recently produced [[liquid helium]] as a [[refrigerant]]. At the temperature of 4.2&nbsp;K, he observed that the resistance abruptly disappeared.<ref>
{{cite journal
|author = H. K. Onnes
|year = 1911
|title = The resistance of pure mercury at helium temperatures
|journal = [[Commun. Phys. Lab. Univ. Leiden]]
|volume = 12 |page = 120
|doi=
}}</ref> In the same experiment, he also observed the [[superfluid]] transition of helium at 2.2&nbsp;K, without recognizing its significance. The precise date and circumstances of the discovery were only reconstructed a century later, when Onnes's notebook was found.<ref>[http://ilorentz.org/history/cold/DelftKes_HKO_PT.pdf The Discovery of Superconductivity]</ref> In subsequent decades, superconductivity was observed in several other materials. In 1913, [[lead]] was found to superconduct at 7&nbsp;K, and in 1941 [[niobium nitride]] was found to superconduct at 16&nbsp;K.
 
Great efforts have been devoted to finding out how and why superconductivity works; the important step occurred in 1933, when [[Walter Meissner|Meissner]] and [[Robert Ochsenfeld|Ochsenfeld]] discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the [[Meissner effect]].<ref>
{{cite journal
|author = W. Meissner and R. Ochsenfeld
|year = 1933
|title = Ein neuer Effekt bei Eintritt der Supraleitfähigkeit
|journal = [[Naturwissenschaften]]
|volume = 21 |issue = 44 |pages = 787–788
|doi = 10.1007/BF01504252
|bibcode = 1933NW.....21..787M }}</ref> In 1935, [[Fritz London|Fritz]] and [[Heinz London]] showed that the Meissner effect was a consequence of the minimization of the electromagnetic [[thermodynamic free energy|free energy]] carried by superconducting current.<ref>{{cite journal
|author = F. London and H. London
|year = 1935
|title = The Electromagnetic Equations of the Supraconductor
|journal = [[Proceedings of the Royal Society of London A]]
|volume = 149 |issue = 866 |pages = 71–88
|doi = 10.1098/rspa.1935.0048
|jstor=96265
|bibcode = 1935RSPSA.149...71L }}</ref>
 
===London theory===
The first phenomenological theory of superconductivity was [[London equations|London theory]]. It was put forward by the brothers Fritz and Heinz London in 1935, shortly after the discovery that magnetic fields are expelled from superconductors. A major triumph of the equations of this theory is their ability to explain the [[Meissner effect]],<ref>{{cite journal
|last= Meissner
|first= W.
|title=Ein neuer Effekt bei Eintritt der Supraleitfähigkeit
|coauthors= R. Ochsenfeld
|journal= Naturwissenschaften
|volume= 21
|year= 1933
|doi= 10.1007/BF01504252
|page= 787 |bibcode = 1933NW.....21..787M
|issue= 44 }}
</ref> wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold. By using the London equation, one can obtain the dependence of the magnetic field inside the superconductor on the distance to the surface.<ref>{{cite web
|url = http://openlearn.open.ac.uk/mod/oucontent/view.php?id=398540&section=3.3
|title = The London equations
|publisher = The Open University
|accessdate  = 2011-10-16}}</ref>
 
There are two London equations:
:<math>\frac{\partial \mathbf{j}_s}{\partial t} = \frac{n_s e^2}{m}\mathbf{E}, \qquad \mathbf{\nabla}\times\mathbf{j}_s =-\frac{n_s e^2}{m}\mathbf{B}. </math>
The first equation follows from [[Newton's second law]] for superconducting electrons.
 
=== Conventional theories (1950s) ===
During the 1950s, theoretical [[condensed matter physics|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).<ref>
{{cite journal
|author = J. Bardeen, L. N. Cooper and J. R. Schrieffer
|year = 1957
|title = Microscopic Theory of Superconductivity
|journal = [[Physical Review]]
|volume = 106 |issue = 1 |pages = 162–164
|doi = 10.1103/PhysRev.106.162
|bibcode = 1957PhRv..106..162B }}</ref><ref name=BardeenCooperSchrieffer>
{{cite journal
|author = J. Bardeen, L. N. Cooper and J. R. Schrieffer
|year = 1957
|title = Theory of Superconductivity
|journal = [[Physical Review]]
|volume = 108 |issue = 5 |pages = 1175–1205
|doi = 10.1103/PhysRev.108.1175|bibcode = 1957PhRv..108.1175B }}</ref>
 
In 1950, the [[phenomenology (science)|phenomenological]] [[Ginzburg-Landau theory]] of superconductivity was devised by [[Lev Davidovich Landau|Landau]] and [[Vitalij Lazarevics Ginzburg|Ginzburg]].<ref>{{cite journal
|author = V. L. Ginzburg and L.D. Landau
|year = 1950
|title = On the theory of superconductivity
|journal = [[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]]
|volume = 20 |page = 1064
}}</ref> This theory, which combined Landau's theory of second-order [[phase transition]]s with a [[Schrödinger equation|Schrödinger]]-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, [[Alexei Alexeevich Abrikosov|Abrikosov]] showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type&nbsp;I and Type&nbsp;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). The four-dimensional extension of the Ginzburg-Landau theory, the [[Coleman-Weinberg potential|Coleman-Weinberg model]], is important in [[quantum field theory]] and [[cosmology]].
 
Also in 1950, Maxwell and Reynolds ''et al.'' found that the critical temperature of a superconductor depends on the [[isotope|isotopic mass]] of the constituent [[chemical element|element]].<ref>
{{cite journal
|author = E. Maxwell
|year = 1950
|title = Isotope Effect in the Superconductivity of Mercury
|journal = [[Physical Review]]
|volume = 78 |issue = 4 |page = 477
|doi =10.1103/PhysRev.78.477
|bibcode = 1950PhRv...78..477M }}</ref><ref>
{{cite journal
|author = C. A. Reynolds, B. Serin, W. H. Wright and L. B. Nesbitt
|year = 1950
|title = Superconductivity of Isotopes of Mercury
|journal = [[Physical Review]]
|volume = 78 |issue = 4 |page = 487
|doi = 10.1103/PhysRev.78.487
|bibcode = 1950PhRv...78..487R }}</ref> 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 [[John Bardeen|Bardeen]], [[Leon Neil Cooper|Cooper]] and [[John Robert Schrieffer|Schrieffer]].<ref name=BardeenCooperSchrieffer/> This BCS theory explained the superconducting current as a [[superfluid]] of [[Cooper pair]]s, 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 [[N. N. Bogolyubov]] 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 (quantum mechanics)|Hamiltonian]].<ref>
{{cite journal
|author = N. N. Bogoliubov
|year = 1958
|title = A new method in the theory of superconductivity
|journal = [[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]]
|volume = 34 |page = 58
}}</ref> In 1959, [[Lev Gor'kov]] showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.<ref>{{cite journal
|author = L. P. Gor'kov
|year = 1959
|title = Microscopic derivation of the Ginzburg—Landau equations in the theory of superconductivity
|journal = [[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]]
|volume = 36 |page = 1364
}}</ref>
 
Generalizations of BCS theory for conventional superconductors form the basis for understanding of the phenomenon of [[superfluidity]], because they fall into the [[Lambda transition]] universality class. The extent to which such generalizations can be applied to [[unconventional superconductor]]s is still controversial.
 
=== Further history ===
The first practical application of superconductivity was developed in 1954 with [[Dudley Allen Buck]]'s invention of the [[cryotron]].<ref>http://dome.mit.edu/bitstream/handle/1721.3/40618/MC665_r15_M-3843.pdf</ref>  Two superconductors with greatly different values of critical magnetic field are combined to produce a fast, simple, switch for computer elements.
 
In 1962, the first commercial superconducting wire, a [[niobium]]-[[titanium]] alloy, was developed by researchers at [[Westinghouse Electric Corporation|Westinghouse]], allowing the construction of the first practical [[superconducting magnet]]s. In the same year, [[Brian David Josephson|Josephson]] made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator.<ref>
{{cite journal
|author = B. D. Josephson
|year = 1962
|title = Possible new effects in superconductive tunnelling
|journal = [[Physics Letters]]
|volume = 1 |issue=7 |pages = 251–253
|doi = 10.1016/0031-9163(62)91369-0
|bibcode = 1962PhL.....1..251J }}</ref> This phenomenon, now called the [[Josephson effect]], is exploited by superconducting devices such as [[SQUID]]s. It is used in the most accurate available measurements of the [[magnetic flux quantum]] ''Φ''<sub>0</sub>&nbsp;=&nbsp;''h''/(2''e''), where ''h'' is the [[Planck constant]]. Coupled with the [[quantum Hall effect|quantum Hall resistivity]], this leads to a precise measurement of the Planck constant. Josephson was awarded the Nobel Prize for this work in 1973.
 
In 2008, it was proposed that the same mechanism that produces superconductivity could produce a [[superinsulator]] state in some materials, with almost infinite [[electrical resistance]].<ref>
{{cite web
| title = Newly discovered fundamental state of matter, a superinsulator, has been created.
| publisher = Science Daily
| date = April 9, 2008
| url = http://www.sciencedaily.com/releases/2008/04/080408160614.htm
| accessdate = 2008-10-23
}}</ref>
 
==High-temperature superconductivity==
[[File:Sc history.gif|right|thumb|340px|Timeline of superconducting materials]]
{{Main|High-temperature superconductivity}}
Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30&nbsp;K. In that year, [[Johannes Georg Bednorz|Bednorz]] and [[K. Alex Müller|Müller]] discovered superconductivity in a [[lanthanum]]-based cuprate [[Perovskite (structure)|perovskite]] material, which had a transition temperature of 35&nbsp;K (Nobel Prize in Physics, 1987).<ref name=Bednorz/> It was soon found that replacing the lanthanum with [[yttrium]] (i.e.,&nbsp;making [[YBCO]]) raised the critical temperature to 92&nbsp;K.<ref name="wu"/>
 
This temperature jump is particularly significant, since it allows [[liquid nitrogen]] as a refrigerant, replacing [[liquid helium]].<ref name="wu">{{cite journal
|author = M. K. Wu ''et al.''
|year = 1987
|title = Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure
|journal = [[Physical Review Letters]]
|volume = 58 |issue = 9 |pages = 908–910
|doi = 10.1103/PhysRevLett.58.908
|pmid = 10035069
|bibcode=1987PhRvL..58..908W
}}</ref>
This can be important commercially because liquid nitrogen can be produced relatively cheaply, even on-site, avoiding some of the problems (such as so-called "solid air" plugs) which arise when liquid helium is used in piping.<ref>{{cite web
| url= http://cryo.gsfc.nasa.gov/introduction/liquid_helium.html
|title=Introduction to Liquid Helium
|work="Cryogenics and Fluid Branch"
|publisher=Goddard Space Flight Center, NASA
}}</ref><ref>{{cite web
|url=http://www.2genterprises.com/cryo_manual_4.html
|title=Section 4.1 "Air plug in the fill line"
|work="Superconducting Rock Magnetometer Cryogenic System Manual"
|publisher=2G Enterprises
|accessdate=9 October 2012
|archiveurl=http://web.archive.org/web/20090506030203/http://www.2genterprises.com/cryo_manual_4.html
|archivedate=May 6, 2009}}</ref>
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]].<ref>
{{cite web
|author = Alexei A. Abrikosov
|url = http://nobelprize.org/nobel_prizes/physics/laureates/2003/abrikosov-lecture.html
|title=type II Superconductors and the Vortex Lattice
|work=Nobel Lecture
|date=8 December 2003
}}</ref>
 
Since about 1993, the highest temperature superconductor was a ceramic material consisting of mercury, barium, calcium, copper and oxygen (HgBa<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>8+δ</sub>) with ''T''<sub>c</sub>&nbsp;= 133–138 K.<ref name="aschi">
{{cite journal
|author=A. Schilling ''et al.''
|year=1993
|title=Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system
|journal = [[Nature (journal)|Nature]]
|volume=363 |issue=6424 |page=56
|doi=10.1038/363056a0
|bibcode = 1993Natur.363..56C}}</ref><ref>
{{cite journal
|author = P. Dai, B. C. Chakoumakos, G. F. Sun, K. W. Wong, Y. Xin and D. F. Lu
|year = 1995
|title = Synthesis and neutron powder diffraction study of the superconductor HgBa<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>8+δ</sub> by Tl substitution
|journal = [[Physica C]]
|volume = 243  |issue = 3–4 |pages = 201–206
|doi = 10.1016/0921-4534(94)02461-8
|bibcode = 1995PhyC..243..201D }}</ref> The latter experiment (138 K) still awaits experimental confirmation, however.
 
In February 2008, an iron-based family of high-temperature superconductors was discovered.<ref>
{{cite journal
|author = Hiroki Takahashi, Kazumi Igawa, Kazunobu Arii, Yoichi Kamihara, Masahiro Hirano, Hideo Hosono
|year = 2008
|title = Superconductivity at 43 K in an iron-based layered compound LaO<sub>1−x</sub>F<sub>x</sub>FeAs
|journal = [[Nature (journal)|Nature]]
|volume = 453  |issue = 7193 |pages = 376–378
|doi = 10.1038/nature06972
|pmid = 18432191
|bibcode = 2008Natur.453..376T }}</ref><ref>
{{cite web
|author=Adrian Cho
|title=Second Family of High-Temperature Superconductors Discovered
|url=http://sciencenow.sciencemag.org/cgi/content/full/2008/417/1
|publisher=ScienceNOW Daily News
}}</ref> Hideo Hosono, of the [[Tokyo Institute of Technology]], and colleagues found lanthanum oxygen fluorine iron arsenide (LaO<sub>1-x</sub>F<sub>x</sub>FeAs), an [[oxypnictide]] that superconducts below 26&nbsp;K. Replacing the lanthanum in LaO<sub>1−''x''</sub>F<sub>''x''</sub>FeAs with [[samarium]] leads to superconductors that work at 55&nbsp;K.<ref>
{{cite journal
|author = Zhi-An Ren ''et al.''
|year = 2008
|title = Superconductivity and phase diagram in iron-based arsenic-oxides ReFeAsO1-d (Re = rare-earth metal) without fluorine doping
|journal = [[EPL (journal)|EPL]]
|volume = 83 |page = 17002
|doi = 10.1209/0295-5075/83/17002
|bibcode = 2008EL.....8317002R |arxiv = 0804.2582 }}</ref>
 
==Applications==
{{Main|Technological applications of superconductivity}}
[[File:Flyingsuperconductor.ogg|thumb|Video of superconducting levitation of [[YBCO]]]]
 
[[Superconducting magnet]]s are some of the most powerful [[electromagnet]]s known. They are used in [[magnetic resonance imaging|MRI]]/[[NMR]] machines, [[mass spectrometer]]s, and the beam-steering magnets used in [[particle accelerator]]s. 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.
 
In the 1950s and 1960s, superconductors were used to build experimental digital computers using [[cryotron]] switches. More recently, superconductors have been used to make [[digital circuit]]s based on [[rapid single flux quantum]] technology and [[RF and microwave filter]]s for [[mobile phone]] base stations.
 
Superconductors are used to build [[Josephson junction]]s which are the building blocks of [[SQUID]]s (superconducting quantum interference devices), the most sensitive [[magnetometer]]s known. SQUIDs are used in [[scanning SQUID microscope]]s and [[magnetoencephalography]]. Series of Josephson devices are used to realize the [[International System of Units|SI]] [[volt]]. Depending on the particular mode of operation, a [[superconductor-insulator-superconductor]] Josephson junction can be used as a photon [[detector]] or as a [[Electronic mixer|mixer]]. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic [[calorimeter|micro-calorimeter]] photon [[detector]]s. The same effect is used in ultrasensitive [[bolometer]]s made from superconducting materials.
 
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]], [[transformer]]s, [[SMES|power storage devices]], [[electric motor]]s (e.g. for vehicle propulsion, as in [[vactrain]]s or [[maglev train]]s), [[magnetic levitation device]]s, [[fault current limiter]]s, nanoscopic materials such as [[buckyballs]], [[Carbon nanotube|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]].
 
==Nobel Prizes for superconductivity==
*[[Heike Kamerlingh Onnes]] (1913), "for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium"
*[[John Bardeen]], [[Leon N. Cooper]], and [[J. Robert Schrieffer]] (1972), "for their jointly developed theory of superconductivity, usually called the BCS-theory"
*[[Leo Esaki]], [[Ivar Giaever]], and [[Brian D. Josephson]] (1973), "for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively," and "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects"
*[[Georg Bednorz]] and [[K. Alex Müller]] (1987), "for their important break-through in the discovery of superconductivity in ceramic materials"
*[[Alexei A. Abrikosov]], [[Vitaly L. Ginzburg]], and [[Anthony J. Leggett]] (2003), "for pioneering contributions to the theory of superconductors and superfluids"<ref name="Nobel Prizes in Physics">{{cite web|title=Nobel Prizes in Physics|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/}}</ref>
 
==See also==
{{colbegin|3}}
*[[Andreev reflection]]
*[[Charge transfer complex]]
*[[Color superconductivity]] in quarks
*[[Composite Reaction Texturing]]
*[[Conventional superconductor]]
*[[Covalent superconductors]]
*[[Flux pumping]]
*[[High-temperature superconductivity]]
*[[Homes's law]]
*[[Iron-based superconductor]]
*[[Kondo effect]]
*[[List of superconductors]]
*[[Little-Parks effect]]
*[[Magnetic levitation]]
*[[Macroscopic quantum phenomena]]
*[[Magnetic sail]]
*[[National Superconducting Cyclotron Laboratory]]
*[[Oxypnictide]]
*[[Persistent current]]
*[[Proximity effect (superconductivity)|Proximity effect]]
*[[Room-temperature superconductor]]
*[[Rutherford cable]]
*[[Spallation Neutron Source]]
*[[Superconducting RF]]
*[[Superconductor classification]]
*[[Superfluid film]]
*[[Superstripes]]
*[[Technological applications of superconductivity]]
*[[Timeline of low-temperature technology]]
*[[Type-I superconductor]]
*[[Type-II superconductor]]
*[[Unconventional superconductor]]
*[[BCS theory]]
*[[Bean's critical state model]]
{{colend}}
 
==References==
{{reflist|2}}
 
==Further reading==
*{{cite book
|author=Hagen Kleinert
|year=1989
|chapter=Superflow and Vortex Lines
|title=Gauge Fields in Condensed Matter
|url=http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html
|volume=1
|publisher=[[World Scientific]]
|isbn=9971-5-0210-0
}}
*{{cite book
|author=Anatoly Larkin; Andrei Varlamov
|year=2005
|title=Theory of Fluctuations in Superconductors
|publisher=[[Oxford University Press]]
|isbn=0-19-852815-9
}}
*{{cite book
|author=A. G. Lebed
|year=2008
|title=The Physics of Organic Superconductors and Conductors
|edition=1st
|publisher=[[Springer (publisher)|Springer]]
|volume=110
|isbn=978-3-540-76667-4
}}
*{{cite book
|author=Jean Matricon, Georges Waysand, Charles Glashausser
|year=2003
|title=The Cold Wars: A History of Superconductivity
|publisher=[[Rutgers University Press]]
|isbn=0-8135-3295-7
}}
*{{cite web
|date=17 August 2006
|title=Physicist Discovers Exotic Superconductivity
|url=http://www.sciencedaily.com/releases/2006/08/060817101658.htm
|publisher=[[ScienceDaily]]
}}
*{{cite book
|author=Michael Tinkham
|title=Introduction to Superconductivity
|edition = 2nd
|publisher=Dover Books
|year=2004
|isbn=0-486-43503-2
}}
*{{cite book
|author=Terry Orlando, Kevin Delin
|year=1991
|title=Foundations of Applied Superconductivity
|publisher=[[Prentice Hall]]
|isbn=978-0-201-18323-8
}}
*{{cite book
|author=Paul Tipler, Ralph Llewellyn
|year=2002
|title=Modern Physics
|edition = 4th
|publisher=[[W. H. Freeman]]
|isbn=0-7167-4345-0
}}
 
==External links==
*[http://www.superconductivity.eu Everything about superconductivity: properties, research, applications with videos, animations, games]
*[http://alfredleitner.com Video about Type I Superconductors: R=0/transition temperatures/ B is a state variable/ Meissner effect/ Energy gap(Giaever)/ BCS model]
*[http://www.magnet.fsu.edu/education/tutorials/magnetacademy/superconductivity101/ Superconductivity: Current in a Cape and Thermal Tights. An introduction to the topic for non-scientists] National High Magnetic Field Laboratory
*[http://www.ornl.gov/reports/m/ornlm3063r1/pt1.html Introduction to superconductivity]
*[http://www.msm.cam.ac.uk/ascg/lectures/ Lectures on Superconductivity (series of videos, including interviews with leading experts)]
*[http://www.superlife.info Superconductivity in everyday life : Interactive exhibition]
*[http://h0.web.u-psud.fr/supraconductivite/vulgaFilms.html Videos for various types of superconducting levitations including trains and hoolahoops – also videos of Ohm's law in a superconductor]
*[http://web.njit.edu/~mathclub/superconductor/index.html Video of the Meissner effect from the NJIT Mathclub]
*[http://www.superconductivitynewsupdate.com Superconductivity News Update]
*[http://www.superconductorweek.com Superconductor Week Newsletter – industry news, links, et cetera]
*[http://www.maniacworld.com/Superconducting-Magnetic-Levitation.html Superconducting Magnetic Levitation]
*[http://www.nscl.msu.edu National Superconducting Cyclotron Laboratory at Michigan State University]
*[http://www.suptech.com/hts_crfe_tech.htm High Temperature Superconducting and Cryogenics in RF applications]
*[http://sdb-server.cern.ch/mediawiki/index.php/Main_Page CERN Superconductors Database]
*[http://www.fluxpump.co.uk/default.aspx Magnetisation of High Temperature superconductors by the flux pumping method]
*[http://youtube.com/watch?v=indyz6O-Xyw&feature=user YouTube Video Levitating magnet]
*[http://www.physics.csulb.edu/~abill/isotope.html Isotope effect in superconductivity]
*[http://www.iop.org/EJ/toc/1468-6996/9/4 International Workshop on superconductivity in Diamond and Related Materials (free download papers)]
*[http://www.nims.go.jp/NFM/NDFCT17/NDFCT17.html New Diamond and Frontier Carbon Technology Volume 17, No.1 Special Issue on Superconductivity in CVD Diamond]
*[http://www.doitpoms.ac.uk/tlplib/superconductivity/index.php DoITPoMS Teaching and Learning Package – "Superconductivity"]
*[http://math.ucr.edu/home/baez/physics/Administrivia/nobel.html The Nobel Prize for Physics, 1901–2008]
*[http://hebergement.u-psud.fr/supraconductivite/pliages_en.html folding hands-on activities about superconductivity]
 
{{States of matter}}
 
[[Category:Phases of matter]]
[[Category:Quark matter]]
[[Category:Exotic matter]]
[[Category:Unsolved problems in physics]]
[[Category:Magnetic levitation]]
[[Category:Superconductivity| ]]
[[Category:Concepts in physics]]
[[Category:Spintronics]]
[[Category:Phase transitions]]
[[Category:Articles containing video clips]]
 
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