Editing Superconductivity (section)

== History ==
{{Main|History of superconductivity}}
[[File:Timeline_of_Superconductivity_from_1900_to_2015.svg|thumb|Timeline of superconducting materials. Colors represent different classes of materials: {{Unbulleted list|list_style=margin-left: 2em;|{{Legend|#acc294|[[:w:BCS theory|BCS]] (dark green circle)|css=border:2px solid #458234}}|{{Legend|#dbef9C|[[:w:Heavy fermion material|Heavy fermion-based]] (light green star)|css=border:2px solid #a6d71c}}|{{Legend|#bddef5|[[:w:Cuprate superconductor|Cuprate]] (blue diamond)|css=border:2px solid #5cb4e8}}|{{Legend|#cfa1d6|[[:w:Buckminsterfullerene|Buckminsterfullerene]]-based (purple inverted triangle)|css=border:2px solid #95329d}}|{{Legend|#f79aaa|[[:w:Carbon|Carbon]]-[[:w:allotrope|allotrope]] (red triangle)|css=border:2px solid #ed0e58}}|{{Legend|#fddfa2|[[:w:Iron|Iron]]-[[:w:pnictogen|pnictogen]]-based (orange square)|css=border:2px solid #fab42c}}|{{Legend|#b3b3b3ff|[[:w:Strontium ruthenate|Strontium ruthenate]] (grey pentagon)|css=border:2px solid #4d4d4dff}}|{{Legend|#ff55ffff|[[:w:Nickel|Nickel]]-based (pink six-point star)|css=border:2px solid #800080ff}}}}]]
[[File:Ehrenfest_Lorentz_Bohr_Kamerlingh_Onnes.jpg|thumb|Heike Kamerlingh Onnes (right), the discoverer of superconductivity. [[Paul Ehrenfest]], [[Hendrik Lorentz]], [[Niels Bohr]] stand to his left.]]
Superconductivity was discovered on April 8, 1911, by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at [[cryogenic]] temperatures using the recently produced [[liquid helium]] as a [[refrigerant]].<ref>{{Cite journal |last1=van Delft |first1=Dirk |last2=Kes |first2=Peter |date=2010-09-01 |title=The discovery of superconductivity |url=https://www.europhysicsnews.org/10.1051/epn/2011104/pdf |journal=[[Physics Today]] |volume=63 |issue=9 |pages=38–43 |bibcode=2010PhT....63i..38V |doi=10.1063/1.3490499 |issn=0031-9228 |doi-access=free}}</ref> At the temperature of 4.2&nbsp;K, he observed that the resistance abruptly disappeared.<ref>{{cite journal |last1=Kamerlingh Onnes |first1=Heike |date=1911 |title=Further experiments with liquid helium. C. On the change of electric resistance of pure metals at very low temperatures etc. IV. The resistance of pure mercury at helium temperatures |url=http://www.dwc.knaw.nl/toegangen/digital-library-knaw/?pagetype=publDetail&pId=PU00013358&lang=en |journal=Proceedings of the Section of Sciences |volume=13 |pages=1274–1276 |bibcode=1910KNAB...13.1274K}}</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>{{cite journal |author=vanDelft |first1=Dirk |last2=Kes |first2=Peter |date=September 2010 |title=The Discovery of Superconductivity |url=http://ilorentz.org/history/cold/DelftKes_HKO_PT.pdf |journal=Physics Today |volume=63 |issue=9 |pages=38–43 |bibcode=2010PhT....63i..38V |doi=10.1063/1.3490499}}</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 [[Walther 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 name="MeissnerOchsenfeld2">{{cite journal |author=Meissner |first1=W. |last2=Ochsenfeld |first2=R. |name-list-style=amp |date=1933 |title=Ein neuer Effekt bei Eintritt der Supraleitfähigkeit |journal=[[Naturwissenschaften]] |volume=21 |issue=44 |pages=787–788 |bibcode=1933NW.....21..787M |doi=10.1007/BF01504252 |s2cid=37842752}}</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=London |first1=F. |last2=London |first2=H. |name-list-style=amp |date=1935 |title=The Electromagnetic Equations of the Supraconductor |journal=[[Proceedings of the Royal Society of London A]] |volume=149 |issue=866 |pages=71–88 |bibcode=1935RSPSA.149...71L |doi=10.1098/rspa.1935.0048 |jstor=96265 |doi-access=}}</ref>

=== London constitutive equations===
The theoretical model that was first conceived for superconductivity was completely classical: it is summarized by [[London equations|London constitutive equations]]. 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 name="MeissnerOchsenfeld2" /> 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 |title=The London equations |url=http://openlearn.open.ac.uk/mod/oucontent/view.php?id=398540&section=3.3 |url-status=dead |archive-url=https://archive.today/20121223034603/http://openlearn.open.ac.uk/mod/oucontent/view.php?id=398540&section=3.3 |archive-date=December 23, 2012 |access-date=2011-10-16 |publisher=The Open University}}</ref>

The two constitutive equations for a superconductor by London are:

<math display="block">\frac{\partial \mathbf{j}}{\partial t} = \frac{n e^2}{m}\mathbf{E}, \qquad \mathbf{\nabla}\times\mathbf{j} =-\frac{n 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 an 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=Bardeen |first1=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |name-list-style=amp |date=1957 |title=Microscopic Theory of Superconductivity |journal=[[Physical Review]] |volume=106 |issue=1 |pages=162–164 |bibcode=1957PhRv..106..162B |doi=10.1103/PhysRev.106.162 |doi-access=free}}</ref><ref name="BardeenCooperSchrieffer2">{{cite journal |author=Bardeen |first1=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |name-list-style=amp |date=1957 |title=Theory of Superconductivity |journal=[[Physical Review]] |volume=108 |issue=5 |pages=1175–1205 |bibcode=1957PhRv..108.1175B |doi=10.1103/PhysRev.108.1175 |doi-access=free}}</ref>

In 1950, the [[Phenomenology (particle physics)|phenomenological]] [[Ginzburg–Landau theory]] of superconductivity was devised by [[Lev Landau|Landau]] and [[Vitaly Ginzburg|Ginzburg]].<ref>{{cite journal |author=Ginzburg |first1=V. L. |last2=Landau |first2=L. D. |name-list-style=amp |date=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 transitions with a [[Schrödinger equation|Schrödinger]]-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, [[Alexei Alexeyevich 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 element.<ref>{{cite journal |author=Maxwell |first=E. |date=1950 |title=Isotope Effect in the Superconductivity of Mercury |journal=[[Physical Review]] |volume=78 |issue=4 |page=477 |bibcode=1950PhRv...78..477M |doi=10.1103/PhysRev.78.477}}</ref><ref>{{cite journal |author=Reynolds |first1=C. A. |last2=Serin |first2=B. |last3=Wright |first3=W. H. |last4=Nesbitt |first4=L. B. |name-list-style=amp |date=1950 |title=Superconductivity of Isotopes of Mercury |journal=[[Physical Review]] |volume=78 |issue=4 |page=487 |bibcode=1950PhRv...78..487R |doi=10.1103/PhysRev.78.487}}</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="BardeenCooperSchrieffer2" /> 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 [[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=Bogoliubov |first=N. N. |date=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=Gor'kov |first=L. P. |date=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><ref name="BCS-boboliubov2">{{cite journal |author=Combescot |first1=M. |last2=Pogosov |first2=W. V. |last3=Betbeder-Matibet |first3=O. |date=2013 |title=BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson–Gaudin exact wave function |journal=Physica C: Superconductivity |volume=485 |pages=47–57 |arxiv=1111.4781 |bibcode=2013PhyC..485...47C |doi=10.1016/j.physc.2012.10.011 |s2cid=119121639}}</ref>

Generalizations of BCS theory for conventional superconductors form the basis for the 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|unconventional superconductors]] is still controversial.

=== Niobium ===
The first practical application of superconductivity was developed in 1954 with [[Dudley Allen Buck]]'s invention of the [[cryotron]].<ref name="mit-memo2">{{cite web |last1=Buck |first1=Dudley A. |title=The Cryotron – A Superconductive Computer Component |url=http://dome.mit.edu/bitstream/handle/1721.3/40618/MC665_r15_M-3843.pdf |access-date=10 August 2014 |publisher=Lincoln Laboratory, Massachusetts Institute of Technology}}</ref> Two superconductors with greatly different values of the critical magnetic field are combined to produce a fast, simple switch for computer elements.

Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, G. B. Yntema<ref>{{cite journal |author=Yntema |first=G. B. |date=1955 |title=Superconducting Winding for Electromagnet |journal=[[Physical Review]] |volume=98 |issue=4 |page=1197 |bibcode=1955PhRv...98.1144. |doi=10.1103/PhysRev.98.1144}}</ref> succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, [[John Eugene Kunzler|J. E. Kunzler]], E. Buehler, F. S. L. Hsu, and J. H. Wernick<ref>{{cite journal |author=Kunzler |first1=J. E. |last2=Buehler |first2=E. |last3=Hsu |first3=F. L. S. |last4=Wernick |first4=J. H. |date=1961 |title=Superconductivity in Nb3Sn at High Current Density in a Magnetic Field of 88 kgauss |journal=Physical Review Letters |volume=6 |issue=3 |pages=89–91 |bibcode=1961PhRvL...6...89K |doi=10.1103/PhysRevLett.6.89}}</ref> made the startling discovery that, at 4.2 kelvin, [[niobium–tin]], a compound consisting of three parts niobium and one part tin, was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 tesla. The alloy was brittle and difficult to fabricate, but niobium–tin proved useful for generating magnetic fields as high as 20 tesla.

In 1962, T. G. Berlincourt and R. R. Hake<ref>{{cite journal |author=Berlincourt |first1=T. G. |last2=Hake |first2=R. R. |name-list-style=amp |date=1962 |title=Pulsed-Magnetic-Field Studies of Superconducting Transition Metal Alloys at High and Low Current Densities |journal=Bulletin of the American Physical Society |volume=II-7 |page=408}}</ref><ref>{{cite journal |author=Berlincourt |first=T. G. |date=1987 |title=Emergence of Nb-Ti as Supermagnet Material |url=http://fs.magnet.fsu.edu/~lee/superconductor-history_files/Centennial_Supplemental/11_2_Nb-Ti_from_beginnings_to_perfection-fullreferences.pdf |journal=Cryogenics |volume=27 |issue=6 |pages=283–289 |bibcode=1987Cryo...27..283B |doi=10.1016/0011-2275(87)90057-9}}</ref> discovered that more ductile alloys of niobium and titanium are suitable for applications up to 10 tesla. Commercial production of [[niobium–titanium]] supermagnet wire immediately commenced at [[Westinghouse Electric Corporation]] and at [[Wah Chang Corporation]]. Although niobium–titanium boasts less-impressive superconducting properties than those of niobium–tin, niobium–titanium became the most widely used "workhorse" supermagnet material, in large measure a consequence of its very high [[ductility]] and ease of fabrication. However, both niobium–tin and niobium–titanium found wide application in MRI medical imagers, bending and focusing magnets for enormous high-energy-particle accelerators, and other applications. Conectus, a European superconductivity consortium, estimated that in 2014, global economic activity for which superconductivity was indispensable amounted to about five billion euros, with MRI systems accounting for about 80% of that total.

=== Josephson effect ===
In 1962, [[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=Josephson |first=B. D. |date=1962 |title=Possible new effects in superconductive tunnelling |journal=[[Physics Letters]] |volume=1 |issue=7 |pages=251–253 |bibcode=1962PhL.....1..251J |doi=10.1016/0031-9163(62)91369-0}}</ref> This phenomenon, now called the [[Josephson effect]], is exploited by superconducting devices such as [[SQUID|SQUIDs]]. 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.<ref>{{Cite web |title=The Nobel Prize in Physics 1973 |url=https://www.nobelprize.org/prizes/physics/1973/summary/ |url-status=live |archive-url=https://web.archive.org/web/20210325040501/https://www.nobelprize.org/prizes/physics/1973/summary/ |archive-date=Mar 25, 2021 |access-date=2021-03-30 |website=[[Nobel Foundation|NobelPrize.org]] |language=en-US}}</ref>

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 |date=April 9, 2008 |title=Newly discovered fundamental state of matter, a superinsulator, has been created. |url=https://www.sciencedaily.com/releases/2008/04/080408160614.htm |access-date=2008-10-23 |website=Science Daily}}</ref> The first development and study of superconducting [[Bose–Einstein condensate]] (BEC) in 2020 suggested a "smooth transition between" BEC and [[BCS theory|Bardeen-Cooper-Shrieffer]] regimes.<ref>{{cite news |title=Researchers demonstrate a superconductor previously thought impossible |url=https://phys.org/news/2020-11-superconductor-previously-thought-impossible.html |access-date=8 December 2020 |work=phys.org |language=en}}</ref><ref>{{cite journal |last1=Hashimoto |first1=Takahiro |last2=Ota |first2=Yuichi |last3=Tsuzuki |first3=Akihiro |last4=Nagashima |first4=Tsubaki |last5=Fukushima |first5=Akiko |last6=Kasahara |first6=Shigeru |last7=Matsuda |first7=Yuji |last8=Matsuura |first8=Kohei |last9=Mizukami |first9=Yuta |last10=Shibauchi |first10=Takasada |last11=Shin |first11=Shik |last12=Okazaki |first12=Kozo |date=1 November 2020 |title=Bose–Einstein condensation superconductivity induced by disappearance of the nematic state |url= |journal=Science Advances |language=en |volume=6 |issue=45 |pages=eabb9052 |bibcode=2020SciA....6.9052H |doi=10.1126/sciadv.abb9052 |issn=2375-2548 |pmc=7673702 |pmid=33158862}}</ref>

=== 2D materials ===
Multiple types of superconductivity are reported in devices made of [[single-layer materials]]. Some of these materials can switch between conducting, insulating, and other behaviors.<ref name=":0">{{Cite web |last=Wood |first=Charlie |date=2024-12-06 |title=Exotic New Superconductors Delight and Confound |url=https://www.quantamagazine.org/exotic-new-superconductors-delight-and-confound-20241206/ |access-date=2025-04-17 |website=Quanta Magazine |language=en}}</ref>

Twisting materials imbues them with a “[[moiré]]” pattern involving tiled hexagonal cells that act like atoms and host electrons. In this environment, the electrons move slowly enough for their collective interactions to guide their behavior. When each cell has a single electron, the electrons take on an antiferromagnetic arrangement; each electron can have a preferred location and magnetic orientation. Their intrinsic magnetic fields tend to alternate between pointing up and down. Adding electrons allows superconductivity by causing Cooper pairs to form. Fu and Schrade argued that electron-on-electron action was allowing both antiferromagnetic and superconducting states.<ref>{{Cite journal |last=Rini |first=Matteo |date=2022-03-16 |title=Explaining Superconductivity in 2D Materials |url=https://physics.aps.org/articles/v15/s36 |journal=Physics |language=en |volume=15 |pages=s36 |doi=10.1103/PhysRevB.105.094506|arxiv=2112.03950 }}</ref>

The first success with 2D materials involved a twisted bilayer graphene sheet (2018, Tc ~1.7 K, 1.1° twist). A twisted three-layer graphene device was later shown to superconduct (2021, Tc ~2.8 K). Then an untwisted trilayer graphene device was reported to superconduct (2022, Tc 1-2 K). The latter was later shown to be tunable, easily reproducing behavior found millions of other configurations. Directly observing what happens when electrons are added to a material or slightly weakening its electric field lets physicists quickly try out an unprecedented number of recipes to see which lead to superconductivity.<ref name=":0" />

These devices have applications i.n [[quantum computing]].

2D materials other than graphene have also been made to superconduct. [[Transition metal dichalcogenides|Transition metal dichalcogenide]] (TMD) sheets twisted at 5 degrees intermittently achieved superconduction. by creating a Josephson junction. The device used used thin layers of [[palladium]] to connect to the sides of a [[tungsten telluride]] layer surrounded and protected by [[boron nitride]].<ref>{{Cite web |last=RIKEN |title=A superconducting junction made from a single 2D material promises to harness strange new physics |url=https://phys.org/news/2023-12-superconducting-junction-2d-material-harness.html |access-date=2025-04-21 |website=phys.org |language=en}}</ref> Another group demonstrated superconduction in [[molybdenum telluride]] (MoTe₂) in 2D [[Van der Waals molecule|van der Waals]] materials using ferroelectric domain walls. The Tc was implied to be higher than typical TMDs (~5–10 K).<ref>{{Cite web |date=2025-01-11 |title=New Link Found Between Ferroelectric Domain Walls and Superconductivity in 2D Materials |url=https://www.gadgets360.com/science/news/new-link-between-ferroelectric-domain-walls-and-superconductivity-in-2d-materials-7441719 |access-date=2025-04-21 |website=Gadgets 360 |language=en}}</ref>

A Cornell group added a 3.5-degree twist to an insulator that allowed electrons to slow down and interact strongly, leaving one electron per cell, exhibiting superconduction. Existing theories do not explain this behavior.

Fu and collaborators proposed that electrons arranged to form a repeating crystal that allows the electron grid to float independently of the background atomic nuclei allows the electron grid to relax. Its ripples pair electrons the way phonons do, although this is unconfirmed.