View source for High-temperature superconductivity

{{Short description|Superconductive behavior at temperatures much higher than absolute zero}}
{{Distinguish|Room-temperature superconductor}}
[[File:BI2223-piece3 001.jpg|thumb|right|A sample of [[bismuth strontium calcium copper oxide]] (BSCCO), which is currently one of the most practical high-temperature superconductors. Notably, it does not contain [[rare-earth elements|rare-earths]]. BSCCO is a [[cuprate superconductor]] based on [[bismuth]] and [[strontium]]. Thanks to its higher operating temperature, cuprates are now becoming competitors for more ordinary [[niobium]]-based superconductors, as well as [[magnesium diboride]] superconductors.]]

'''High-temperature superconductivity''' ('''high-{{mvar|T}}<sub>c</sub>''' or '''HTS''') is [[superconductivity]] in [[material]]s with a critical temperature (the temperature below which the material behaves as a superconductor) above {{convert|77|K}}, the [[boiling point]] of [[liquid nitrogen]].<ref name=arstechnica:-25-years-on>{{cite news |last=Timmer |first=John |date=May 2011 |title=25&nbsp;years on, the search for higher-temp superconductors continues |newspaper=Ars Technica |url=https://arstechnica.com/science/news/2011/04/25-years-on-the-search-for-higher-temp-superconductors-continues.ars |access-date=March 2, 2012 |url-status=live |archive-url=https://web.archive.org/web/20120304125313/http://arstechnica.com/science/news/2011/04/25-years-on-the-search-for-higher-temp-superconductors-continues.ars |archive-date=March 4, 2012}}</ref> They are "high-temperature" only relative to previously known superconductors, which function only closer to [[absolute zero]]. The first high-temperature superconductor was discovered in 1986 by [[IBM]] researchers [[Georg Bednorz]] and [[K. Alex Müller]].<ref name=pjford>{{cite book |last1=Saunders |first1=P. J. |last2=Ford |first2=G. A. |date=2005 |title=The Rise of the Superconductors |publisher=CRC Press |location=Boca Raton, FL |isbn=0-7484-0772-3}}</ref><ref name=Bedn1986>{{cite journal |last1=Bednorz |first1=J. G. |last2=Müller |first2=K. A. |year=1986 |title=Possible high {{mvar|T}}<sub>c</sub> superconductivity in the Ba-La-Cu-O system |journal=[[Zeitschrift für Physik B]] |volume=64  |issue=2  |pages=189–193 |bibcode=1986ZPhyB..64..189B |doi=10.1007/BF01303701 |s2cid=118314311 }}</ref> Although the critical temperature is around {{convert|35.1|K}}, this material was modified by [[Ching-Wu Chu]] to make the first high-temperature superconductor with critical temperature {{convert|93|K}}.<ref name=YBCO>{{cite journal|title = Superconductivity at 93 K in a New Mixed-Phase Y–Ba–Cu–O Compound System at Ambient Pressure|journal = Physical Review Letters|year = 1987|volume = 58|pages = 908–910|doi = 10.1103/PhysRevLett.58.908|pmid = 10035069|issue = 9|bibcode=1987PhRvL..58..908W|last1 = Wu|first1 = M. K.|last2 = Ashburn|first2 = J. R.|last3 = Torng|first3 = C. J.|last4 = Hor|first4 = P. H.|last5 = Meng|first5 = R. L.|last6 = Gao|first6 = L|last7 = Huang|first7 = Z. J.|last8 = Wang|first8 = Y. Q.|last9 = Chu|first9 = C. W.|doi-access = free}}</ref> Bednorz and Müller were awarded the [[Nobel Prize in Physics]] in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials".<ref>{{cite web |title=1987: J. Georg Bednorz, K. Alex Müller |series=The Nobel Prize in Physics |website=Nobelprize.org |url=http://nobelprize.org/nobel_prizes/physics/laureates/1987/index.html |access-date=April 19, 2012 |archive-url=https://web.archive.org/web/20080919014520/http://nobelprize.org/nobel_prizes/physics/laureates/1987/index.html |archive-date=September 19, 2008}}</ref> Most high-{{mvar|T}}<sub>c</sub> materials are [[type-II superconductor]]s.

The major advantage of high-temperature superconductors is that they can be cooled using liquid nitrogen,<ref name=pjford/> in contrast to previously known superconductors, which require expensive and hard-to-handle coolants, primarily [[liquid helium]]. A second advantage of high-{{mvar|T}}<sub>c</sub> materials is they retain their superconductivity in higher magnetic fields than previous materials. This is important when constructing [[superconducting magnet]]s, a primary application of high-{{mvar|T}}<sub>c</sub> materials.

The majority of high-temperature superconductors are [[ceramic]]s, rather than the previously known metallic materials. Ceramic superconductors are suitable for some practical uses but encounter manufacturing issues. For example, most ceramics are [[brittle]], which complicates wire fabrication.<ref>{{cite book |last=Plakida |first=N. |year=2010 |title=High Temperature Cuprate Superconductors |page=480 |publisher=Springer |isbn=978-3-642-12632-1|series=Springer Series in Solid-State Sciences |url=https://www.springer.com/gp/book/9783642126321}}</ref> 

The main class of high-temperature superconductors is [[copper oxide]]s combined with other metals, especially the [[rare-earth barium copper oxide]]s (REBCOs) such as [[yttrium barium copper oxide]] (YBCO). The second class of high-temperature superconductors in the practical classification is the [[iron-based superconductor|iron-based compounds]].<ref>{{cite news |last=Choi |first=Charles Q. |title=A New Iron Age: New class of superconductor may help pin down mysterious physics |work=Scientific American |url= https://www.scientificamerican.com/article/iron-exposed-as-high-temp-superconductor/ |access-date=October 25, 2019}}</ref><ref name=ren>{{cite journal |last1=Ren |first1=Zhi-An |last2=Che |first2=Guang-Can |last3=Dong |first3=Xiao-Li |last4=Yang |first4=Jie |last5=Lu |first5=Wei |last6=Yi |first6=Wei |last7=Shen |first7=Xiao-Li |last8=Li |first8=Zheng-Cai |last9=Sun |first9=Li-Ling |last10=Zhou |first10=Fang |last11=Zhao |first11=Zhong-Xian |display-authors=6 |year=2008 |title=Superconductivity and phase diagram in iron-based arsenic-oxides ReFeAsO1−δ (Re=rare-earth metal) without fluorine doping |journal=[[EPL (journal)|EPL]] |volume=83  |issue=1  |article-number=17002 |doi=10.1209/0295-5075/83/17002  |bibcode=2008EL.....8317002R |arxiv=0804.2582   |s2cid = 96240327}}</ref> [[Magnesium diboride]] is sometimes included in high-temperature superconductors: It is relatively simple to manufacture, but it superconducts only below {{cvt|39|K|C}}, which makes it unsuitable for liquid nitrogen cooling.

== History ==
[[File:Timeline of Superconductivity from 1900 to 2015.svg|thumb|upright=2|Timeline of superconductor discoveries. On the right one can see the liquid nitrogen temperature, which usually divides superconductors at high from superconductors at low temperatures. [[Cuprate]]s are displayed as blue diamonds, and [[iron-based superconductor]]s as yellow squares. [[Magnesium diboride]] and other low-temperature or high-pressure metallic [[BCS superconductor]]s are displayed for reference as green circles.]]

Superconductivity was discovered by [[Heike Kamerlingh Onnes|Kamerlingh Onnes]] in 1911, in a metal solid. Ever since, researchers have attempted to create superconductivity at higher temperatures<ref name="bbc">{{cite video |people=Nisbett, Alec (producer) |year=1988 |title=Superconductor: The race for the prize |medium=Television Episode}}</ref> with the goal of finding a [[room-temperature superconductor]].<ref>{{cite book |last=Mourachkine|first=A. |year=2004 |title=Room-Temperature Superconductivity |publisher=Cambridge International Science Publishing |arxiv=cond-mat/0606187 |place=Cambridge, UK |id=cond–mat/0606187|isbn=1-904602-27-4|bibcode=2006cond.mat..6187M}}</ref> By the late 1970s, superconductivity was observed in several metallic compounds (in particular [[Niobium|Nb]]-based, such as [[Niobium–titanium|NbTi]], [[Niobium–tin|Nb<sub>3</sub>Sn]], and [[Nb3Ge|Nb<sub>3</sub>Ge]]) at temperatures that were much higher than those for elemental metals and which could even exceed {{convert|20|K|C}}.

In 1986, at the [[IBM]] research lab near [[Zürich]] in Switzerland, Bednorz and Müller were looking for superconductivity in a new class of [[ceramic]]s: the copper oxides, or [[cuprates]]. In that year, [[Johannes Georg Bednorz|Bednorz]] and Müller discovered superconductivity in [[lanthanum barium copper oxide]] (LBCO), 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">{{cite journal |author=Bednorz |first1=J. G. |last2=Müller |first2=K. A. |name-list-style=amp |date=1986 |title=Possible high T<sub>c</sub> superconductivity in the Ba−La−Cu−O system |journal=Z. Phys. B |volume=64 |issue=1 |pages=189–193 |bibcode=1986ZPhyB..64..189B |doi=10.1007/BF01303701 |s2cid=118314311}}</ref> It was soon found that replacing the lanthanum with [[yttrium]] (i.e.,&nbsp;making YBCO) raised the critical temperature above 90&nbsp;K.<ref name="wu">{{cite journal |author=Wu |first=M. K. |display-authors=etal |date=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 |bibcode=1987PhRvL..58..908W |doi=10.1103/PhysRevLett.58.908 |pmid=10035069 |doi-access=free}}</ref> Their results were soon confirmed<ref>{{cite book|editor-first1=Stuart A.|editor-last1=Wolf|editor-first2=Vladimir Z.|editor-last2=Kresin|title=Novel Superconductivity|location=New York|publisher=Plenum Press|orig-date=1987|date=6 December 2012|isbn=978-1-4613-1937-5|url={{GBurl|9KfSBwAAQBAJ}}|access-date=2 August 2023}}</ref> by many groups.<ref name="tanaka01">
{{cite journal
 |last=Tanaka |first=Shoji
 |title=High temperature superconductivity: History and Outlook
 |journal=JSAP International
 |year=2001
 |url=http://www.jsap.or.jp/jsapi/Pdf/Number04/PastPresentFuture.pdf
 |access-date=March 2, 2012|url-status=live
 |archive-url=https://web.archive.org/web/20120816203010/http://www.jsap.or.jp/jsapi/Pdf/Number04/PastPresentFuture.pdf
 |archive-date=August 16, 2012
}}
</ref>

In 1987, [[Philip W. Anderson]] gave the first theoretical description of these materials, based on the [[resonating valence bond theory|resonating valence bond (RVB) theory]],<ref name=Anderson87>
{{cite journal
 |last=Anderson |first=Philip
 |year=1987
 |title=The Resonating Valence Bond State in La<sub>2</sub>CuO<sub>4</sub> and Superconductivity
 |journal=Science
 |volume=235 |issue=4793 |pages=1196–1198
 |bibcode=1987Sci...235.1196A |doi=10.1126/science.235.4793.1196
 |pmid=17818979 |s2cid=28146486
}}
</ref> but a full understanding of these materials is still developing today. These superconductors are now known to possess a ''d''-wave{{clarify|date=June 2014}} pair symmetry. The first proposal that high-temperature cuprate superconductivity involves ''d''-wave pairing was made in 1987 by N. E. Bickers, [[Douglas James Scalapino]] and R. T. Scalettar,<ref name=bickers87>
{{cite journal
 |last1=Bickers    |first1=N. E.
 |last2=Scalapino  |first2=D. J.
 |last3=Scalettar  |first3=R. T.
 |year=1987
 |title=CDW and SDW mediated pairing interactions
 |journal=Int. J. Mod. Phys. B
 |volume=1|issue=3n04|pages=687–695
 |bibcode=1987IJMPB...1..687B|doi=10.1142/S0217979287001079
}}
</ref> followed by three subsequent theories in 1988 by Masahiko Inui, Sebastian Doniach, Peter J. Hirschfeld and Andrei E. Ruckenstein,<ref name=inui88>
{{cite journal |last1=Inui |first1=Masahiko|last2=Doniach |first2=Sebastian |last3=Hirschfeld |first3=Peter J.|last4=Ruckenstein |first4=Andrei E. |last5=Zhao |first5=Z. |last6=Yang |first6=Q. |last7=Ni |first7=Y. |last8=Liu |first8=G. |year=1988 |title=Coexistence of antiferromagnetism and superconductivity in a mean-field theory of high-{{mvar|T}}{{sub|c}} superconductors |journal=Phys. Rev. B |volume=37 |issue=10 |pages=5182–5185 |bibcode=1988PhRvB..37.5182D|doi=10.1103/PhysRevB.37.5182|pmid=9943697 |url=http://prb.aps.org/abstract/PRB/v37/i4/p2320_1|archive-url=https://archive.today/20130703172401/http://prb.aps.org/abstract/PRB/v37/i4/p2320_1 |archive-date=July 3, 2013|url-access=subscription }}</ref> using spin-fluctuation theory, and by [[Claudius Gros]], Didier Poilblanc, Maurice T. Rice and FC. Zhang,<ref name=gros88>
{{cite journal
 |last1=Gros   |first1=Claudius
 |last2=Poilblanc |first2=Didier
 |last3=Rice   |first3=T. Maurice|author3-link=Thomas Maurice Rice
 |last4=Zhang  |first4=F. C. |author4-link=Zhang Fuchun
 |year=1988
 |title=Superconductivity in correlated wavefunctions
 |journal=Physica C
 |volume=153–155 |pages=543–548
 |bibcode=1988PhyC..153..543G |doi=10.1016/0921-4534(88)90715-0
}}</ref> and by [[Gabriel Kotliar]] and Jialin Liu identifying ''d''-wave pairing as a natural consequence of the RVB theory.<ref name=kotliar88>
{{cite journal
 |last1=Kotliar |first1=Gabriel
 |last2=Liu     |first2=Jialin
 |year=1988
 |title=Superexchange mechanism and d-wave superconductivity
 |journal=Physical Review B
 |volume=38 |issue=7 |pages=5142–5145
 |bibcode=1988PhRvB..38.5142K |doi=10.1103/PhysRevB.38.5142 |pmid=9946940
}}
</ref> The confirmation of the ''d''-wave nature of the cuprate superconductors was made by a variety of experiments, including the direct observation of the ''d''-wave nodes in the excitation spectrum through [[Angle-resolved photoemission spectroscopy|angle resolved photoemission spectroscopy]] (ARPES), the observation of a half-integer flux in tunneling experiments, and indirectly from the temperature dependence of the penetration depth, specific heat and thermal conductivity.

Until 2001 the cuprates were thought be the only true high temperature superconductors. In that year MgB<sub>2</sub> with T<sub>c</sub> of 39K was discovered by Akimitsu and colleagues. This was followed in 2006 by Hosono and coworkers with iron-based layered  [[oxypnictide]] compound with T<sub>c</sub> of 56K.<ref>{{Cite journal |last=Kamihara |first=Yoichi |last2=Hiramatsu |first2=Hidenori |last3=Hirano |first3=Masahiro |last4=Kawamura |first4=Ryuto |last5=Yanagi |first5=Hiroshi |last6=Kamiya |first6=Toshio |last7=Hosono |first7=Hideo |date=2006-08-01 |title=Iron-Based Layered Superconductor:  LaOFeP |url=https://pubs.acs.org/doi/10.1021/ja063355c |journal=Journal of the American Chemical Society |volume=128 |issue=31 |pages=10012–10013 |doi=10.1021/ja063355c |issn=0002-7863|url-access=subscription }}</ref> These temperature are below the cuprates but well above the conventional superconductors.<ref name=Bussman-Holder-2020>{{Cite journal |last=Bussmann-Holder |first=Annette |last2=Keller |first2=Hugo |date=2020-02-01 |title=High-temperature superconductors: underlying physics and applications |url=https://www.degruyterbrill.com/document/doi/10.1515/znb-2019-0103/html |journal=Zeitschrift für Naturforschung B |language=en |volume=75 |issue=1-2 |pages=3–14 |doi=10.1515/znb-2019-0103 |issn=1865-7117|arxiv=1911.02303 }}</ref>

In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials was reported by [[École Polytechnique Fédérale de Lausanne]] (EPFL) scientists<ref>
{{cite journal
 |last1=Dalla Piazza |first1=B. |last2=Mourigal |first2=M.
 |last3=Christensen |first3=N. B. |last4=Nilsen |first4=G. J.
 |last5=Tregenna-Piggott |first5=P. |last6=Perring |first6=T. G.
 |last7=Enderle |first7=M. |last8=McMorrow |first8=D. F.
 |last9=Ivanov |first9=D. A. |last10=Rønnow |first10=H. M.
 |display-authors=6
 |year=2015
 |title=Fractional excitations in the square-lattice quantum antiferromagnet
 |journal=Nature Physics
 |volume=11|issue=1|pages=62–68
 |doi=10.1038/nphys3172|pmid=25729400|pmc=4340518|arxiv=1501.01767
 |bibcode=2015NatPh..11...62D
}}
</ref> lending support for Anderson's theory of high-temperature superconductivity.<ref>
{{cite press release
 |title=How electrons split: New evidence of exotic behaviors
 |date=December 23, 2014
 |website=Nanowerk
 |publisher=École Polytechnique Fédérale de Lausanne
 |url=http://www.nanowerk.com/nanotechnology-news/newsid=38557.php
 |access-date=December 23, 2014|url-status=live
 |archive-url=https://web.archive.org/web/20141223224211/http://www.nanowerk.com/nanotechnology-news/newsid=38557.php
 |archive-date=December 23, 2014
}}
</ref> In 2014 and 2015, [[hydrogen sulfide]] ({{chem|H|2|S}}) at extremely high pressures (around 150 gigapascals) was first predicted and then confirmed to be a high-temperature superconductor with a transition temperature of 80&nbsp;K.<ref>{{Cite journal |last1=Li |first1=Yinwei |last2=Hao |first2=Jian |last3=Liu |first3=Hanyu |last4=Li |first4=Yanling |last5=Ma |first5=Yanming |date=2014-05-07 |title=The metallization and superconductivity of dense hydrogen sulfide |journal=The Journal of Chemical Physics |volume=140 |issue=17 |page=174712 |arxiv=1402.2721 |bibcode=2014JChPh.140q4712L |doi=10.1063/1.4874158 |issn=0021-9606 |pmid=24811660 |s2cid=15633660}}</ref><ref name="DrozdovEremets2015">{{cite journal |last1=Drozdov |first1=A. P. |last2=Eremets |first2=M. I. |last3=Troyan |first3=I. A. |last4=Ksenofontov |first4=V. |last5=Shylin |first5=S. I. |year=2015 |title=Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system |journal=Nature |volume=525 |issue=7567 |pages=73–6 |arxiv=1506.08190 |bibcode=2015Natur.525...73D |doi=10.1038/nature14964 |issn=0028-0836 |pmid=26280333 |s2cid=4468914}}</ref><ref name=":02">{{Cite web |last=Wood |first=Charlie |date=14 October 2020 |title=Room-Temperature Superconductivity Achieved for the First Time |url=https://www.quantamagazine.org/physicists-discover-first-room-temperature-superconductor-20201014/ |access-date=2020-10-29 |website=Quanta Magazine |language=en}}</ref> 

In 2018, a research team from the Department of Physics, [[Massachusetts Institute of Technology]], discovered [[Bilayer graphene#Superconductivity in twisted bilayer graphene|superconductivity in bilayer graphene]] with one layer [[Twistronics|twisted at an angle]] of approximately 1.1&nbsp;degrees with cooling and applying a small electric charge. Even if the experiments were not carried out in a high-temperature environment, the results are correlated less to classical but high temperature superconductors, given that no foreign atoms needed to be introduced.<ref>{{Cite journal |last1=Cao |first1=Yuan |author-link1=Yuan Cao |last2=Fatemi |first2=Valla |last3=Demir |first3=Ahmet |last4=Fang |first4=Shiang |last5=Tomarken |first5=Spencer L. |last6=Luo |first6=Jason Y. |last7=Sanchez-Yamagishi |first7=J. D. |last8=Watanabe |first8=K. |last9=Taniguchi |first9=T. |date=2018-03-05 |title=Correlated insulator behaviour at half-filling in magic-angle graphene superlattices |journal=Nature |language=En |volume=556 |issue=7699 |pages=80–84 |arxiv=1802.00553 |bibcode=2018Natur.556...80C |doi=10.1038/nature26154 |issn=1476-4687 |pmid=29512654 |s2cid=4601086}}</ref> The superconductivity effect came about as a result of electrons twisted into a vortex between the graphene layers, called "[[Skyrmion|skyrmions]]". These act as a single particle and can pair up across the graphene's layers, leading to the basic conditions required for superconductivity.<ref>{{Cite web |last=Wood |first=Charlie |date=16 March 2021 |title=A New Twist Reveals Superconductivity's Secrets |url=https://www.quantamagazine.org/graphenes-new-twist-reveals-superconductivitys-secrets-20210316/ |access-date=2021-03-23 |website=Quanta Magazine |language=en}}</ref>

In 2019 it was discovered that [[lanthanum hydride]] ({{chem|La|H|10}}) becomes a superconductor at 250&nbsp;K under a pressure of 170 gigapascals.<ref>{{cite journal |last1=Drozdov |first1=A. P. |last2=Kong |first2=P. P. |last3=Minkov |first3=V. S. |last4=Besedin |first4=S. P. |last5=Kuzovnikov |first5=M. A. |last6=Mozaffari |first6=S. |last7=Balicas |first7=L. |last8=Balakirev |first8=F. F. |last9=Graf |first9=D. E. |last10=Prakapenka |first10=V. B. |last11=Greenberg |first11=E. |last12=Knyazev |first12=D. A. |last13=Tkacz |first13=M. |last14=Eremets |first14=M. I. |year=2019 |title=Superconductivity at 250 K in Lanthanum Hydride under High Pressures |journal=Nature |volume=569 |issue=7757 |pages=528–531 |arxiv=1812.01561 |bibcode=2019Natur.569..528D |doi=10.1038/s41586-019-1201-8 |pmid=31118520 |s2cid=119231000}}</ref><ref name=":02" />

In 2020, a [[room-temperature superconductor]] (critical temperature 288&nbsp;K) made from hydrogen, carbon and sulfur under pressures of around 270 gigapascals was described in a paper in ''Nature''.<ref>{{cite journal |last1=Snider |first1=Eliot |display-authors=etal |date=Oct 14, 2020 |title=Room-temperature superconductivity in a carbonaceous sulfur hydride |url=https://www.osti.gov/biblio/1673473 |journal=Nature |volume=586 |issue=7829 |pages=373–377 |bibcode=2020Natur.586..373S |doi=10.1038/s41586-020-2801-z |osti=1673473 |pmid=33057222 |s2cid=222823227}}{{Retracted|doi=10.1038/s41586-022-05294-9|pmid=36163290|intentional=yes}}</ref><ref>{{cite news |author=Chang |first=Kenneth |date=October 14, 2020 |title=Finally, the First Room-Temperature Superconductor |url=https://www.nytimes.com/2020/10/14/science/superconductor-room-temperature.html |newspaper=The New York Times}}</ref> However, in 2022 the article was [[Retraction in academic publishing|retracted]] by the editors because the validity of background subtraction procedures had been called into question. All nine authors maintain that the raw data strongly support the main claims of the paper.<ref>{{cite journal |last1=Snider |first1=Elliot |last2=Dasenbrock-Gammon |first2=Nathan |last3=McBride |first3=Raymond |last4=Debessai |first4=Mathew |last5=Vindana |first5=Hiranya |last6=Vencatasamy |first6=Kevin |last7=Lawler |first7=Keith V. |last8=Salamat |first8=Ashkan |last9=Dias |first9=Ranga P. |date=26 September 2022 |title=Retraction Note: Room-temperature superconductivity in a carbonaceous sulfur hydride |journal=Nature |volume=610 |issue=7933 |page=804 |bibcode=2022Natur.610..804S |doi=10.1038/s41586-022-05294-9 |pmid=36163290 |s2cid=252544156 |doi-access=free}}</ref>

In 2023 a study reported superconductivity at room temperature and ambient pressure in [[highly oriented pyrolytic graphite]] with dense arrays of nearly parallel line defects.<ref>{{cite journal |last1=Kopelevich |first1=Yakov |last2=Torres |first2=José |last3=Da Silva |first3=Robson |last4=Oliveira |first4=Felipe |last5=Diamantini |first5=Maria Cristina |last6=Trugenberger |first6=Carlo |last7=Vinokur |first7=Valerii |date=2024 |title=Global Room-Temperature Superconductivity in Graphite |url=https://onlinelibrary.wiley.com/doi/10.1002/qute.202300230?ref=upstract.com |journal=Advanced Quantum Technologies |volume=7 |issue=2 |arxiv=2208.00854 |doi=10.1002/qute.202300230}}</ref>

As of 2021,<ref name="cao21" /> the superconductor with the highest transition temperature at [[ambient pressure]] was the cuprate of mercury, barium, and calcium, at around {{cvt|133|K|C}}.<ref name="schilling93">
{{cite journal |last1=Schilling |first1=A. |last2=Cantoni |first2=M. |last3=Guo |first3=J. D. |last4=Ott |first4=H. R. |year=1993 |title=Superconductivity in the Hg–Ba–Ca–Cu–O system |journal=Nature |volume=363 |issue=6424 |pages=56–58 |bibcode=1993Natur.363...56S |doi=10.1038/363056a0 |s2cid=4328716}}
</ref> Other superconductors have higher recorded transition temperatures{{snd}}for example lanthanum superhydride at {{cvt|250|K|C}}, but these only occur at high pressure.<ref name="eremets">
{{cite journal |last1=Drozdov |first1=A. P. |last2=Kong |first2=P. P. |last3=Minkov |first3=V. S. |last4=Besedin |first4=S. P. |last5=Kuzovnikov |first5=M. A. |last6=Mozaffari |first6=S. |last7=Balicas |first7=L. |last8=Balakirev |first8=F. F. |last9=Graf |first9=D. E. |last10=Prakapenka |first10=V. B. |last11=Greenberg |first11=E. |last12=Knyazev |first12=D. A. |last13=Tkacz |first13=M. |last14=Eremets |first14=M. I. |year=2019 |title=Superconductivity at 250&nbsp;K in lanthanum hydride under high pressures |journal=Nature |volume=569 |issue=7757 |pages=528–531 |arxiv=1812.01561 |bibcode=2019Natur.569..528D |doi=10.1038/s41586-019-1201-8 |pmid=31118520 |s2cid=119231000}}
</ref>

== Selected list of superconductors ==
{{legend2|#F9F9F9|Superconductors|border=1px solid #AAAAAA}} {{legend2|#aaeeee|Cooling agents|border=1px solid #AAAAAA}}
{| class="wikitable"
|+Selection of confirmed superconductors and common cooling agents<ref>Report about first room-temperature (15&nbsp;°C) superconductor [[Carbonaceous sulfur hydride|H<sub>2</sub>S + CH<sub>4</sub>]] at 267&nbsp;GPa is not reliable ([[Retraction in academic publishing|retracted]]). ''See'' {{Cite journal
 |last1=Castelvecchi  |first1=Davide    
 |date=2022-09-27
 |title=Room-Stunning room-temperature-superconductor claim is retracted
 |journal=Nature
 |doi=10.1038/d41586-022-03066-z 
 |pmid=36171305 
 |s2cid=252597663 
 |language=en
 |url=https://www.nature.com/articles/d41586-022-03066-z
|url-access=subscription}}</ref>
! colspan="2" |{{mvar|T}}<sub>c</sub>/{{mvar|T}}<sub>boiling</sub>
! rowspan="2" |Pressure
! rowspan="2" |Material
! rowspan="2" |Notes
|-
! K
! °C
|-
|- style="background:#aaeeee"
| 273.15
| 0
| 100 [[kPa]]
| colspan="2" |[[Ice]]: Melting point at atmospheric pressure (common cooling agent; for reference)
|-
| 250
| −23
| 170 [[GPa]]
| [[Lanthanum decahydride|LaH<sub>10</sub>]]<ref name=eremets22>{{cite journal |last1=Eremets |first1=M. I. |last2=Minkov |first2=V. S. |last3=Drozdov |first3=A. P. |last4=Kong |first4=P. P. |last5=Ksenofontov |first5=V. |last6=Shylin |first6=S. I. |last7=Bud'ko |first7=S. L. |last8=Prozorov |first8=R. |last9=Balakirev |first9=F. F. |last10=Sun |first10=Dan |last11=Mozzafari |first11=S. |last12=Balicas |first12=L. |title=High‑Temperature Superconductivity in Hydrides: Experimental Evidence and Details |journal=Journal of Superconductivity and Novel Magnetism |date=10 January 2022 |volume=35 |issue=4 |pages=965–977 |doi=10.1007/s10948-022-06148-1 |doi-access=free |arxiv=2201.05137 }}</ref>
| Metallic superconductor with one of the highest known critical temperatures
|-
| 203
| −70
| 155 GPa
| High pressure phase of [[hydrogen sulfide]] (H<sub>2</sub>S)
| Mechanism unclear, observable [[Kinetic isotope effect|isotope effect]]<ref>
{{cite journal
 |last1=Drozdov |first1=A. P.  |last2=Eremets     |first2=M. I.
 |last3=Troyan  |first3=I. A.  |last4=Ksenofontov |first4=V.
 |last5=Shylin  |first5=S. I.
 |date=September 2015
 |title=Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system
 |journal=Nature
 |volume=525 |issue=7567 |pages=73–76
 |doi=10.1038/nature14964 |pmid=26280333|issn=0028-0836
 |arxiv=1506.08190 |bibcode=2015Natur.525...73D |s2cid=4468914
 |url=http://www.nature.com/articles/nature14964
 |language=en
}}
</ref>
|- style="background:#aaeeee"
| 194.6
| −78.5
| 100 kPa
| colspan="2" |[[Carbon dioxide]] ([[dry ice]]): Sublimation point at atmospheric pressure (common cooling agent; for reference)
|-
| 138
| −135
| 
| Hg<sub>12</sub>Tl<sub>3</sub>Ba<sub>30</sub>Ca<sub>30</sub>Cu<sub>45</sub>O<sub>127</sub><ref name="cao21">{{cite journal |doi=10.1039/d0na00987c|title=Emerging field of few-layered intercalated 2D materials |year=2021 |last1=Cao |first1=Qing |last2=Grote |first2=Fabian |last3=Hußmann |first3=Marleen |last4=Eigler |first4=Siegfried |journal=Nanoscale Advances |volume=3 |issue=4 |pages=963–982 |pmid=36133283 |pmc=9417328 |bibcode=2021NanoA...3..963C }}</ref>
| rowspan="3" |High-temperature superconductors with copper oxide with relatively high critical temperatures
|-
| 110
| −163
|
| Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub> ([[Bismuth strontium calcium copper oxide|BSCCO]])
|-
| 92
| −181
|
| YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub> ([[Yttrium barium copper oxide|YBCO]])
|- style="background:#aaeeee"
| 87
| −186
| 100 kPa
| colspan="2" |[[Argon]]: Boiling point at atmospheric pressure (common cooling agent; for reference)
|- style="background:#aaeeee"
|77
|−196
| 100 kPa
| colspan="2" |[[Nitrogen]]: Boiling point at atmospheric pressure (common cooling agent; for reference)
|-
|45
|−228
|
|SmFeAsO<sub>0.85</sub>F<sub>0.15</sub>
| rowspan="2" |Low-temperature superconductors with relatively high critical temperatures 
|-
|41
|−232
|
|CeOFeAs
|-
| 39
| −234
| 100 kPa
| [[Magnesium diboride|MgB<sub>2</sub>]]
| Metallic superconductor with relatively high critical temperature at atmospheric pressure
|-
| 30
| −243
| 100 kPa
| La<sub>2−x</sub>Ba<sub>x</sub>CuO<sub>4</sub><ref name=":0">
{{Cite web
 |title=Superconductivity Examples
 |website=hyperphysics.phy-astr.gsu.edu
 |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/scex.html
 |access-date=2020-06-14
}}
</ref>
|First high-temperature superconductor with copper oxide, discovered by Bednorz and Müller
|- style="background:#aaeeee"
| 27
| −246
| 100 kPa
| colspan="2" |[[Neon]]: Boiling point at atmospheric pressure (common cooling agent; for reference)
|- style="background:#aaeeee"
| 21.15
| −252
| 100 kPa
| colspan="2" |[[Hydrogen]]: Boiling point at atmospheric pressure (common cooling agent; for reference)
|-
| 18
| −255
|
| Nb<sub>3</sub>Sn<ref name=":0" />
| rowspan="2" |Metallic low-temperature superconductors with technical relevance
|-
| 9.2
| −264.0
|
| NbTi<ref>
{{cite book
 |last1=Flükiger  |first1=R.   |last2=Hariharan |first2=S.Y.
 |last3=Küntzler  |first3=R.   |last4=Luo       |first4=H.L.
 |last5=Weiss     |first5=F.   |last6=Wolf      |first6=T.
 |last7=Xu        |first7=J.Q.
 |year=1994
 |chapter=Nb–Ti
 |title=Materials
 |volume=21b2: Nb–H – Nb–Zr, Nd – Np
 |pages=222–229
 |editor1-last=Flükiger |editor1-first=R.
 |editor2-last=Klose    |editor2-first=W.
 |publisher=Springer-Verlag
 |place=Berlin; Heidelberg
 |doi=10.1007/10423690_53  |isbn=3-540-57541-3
 |url=http://materials.springer.com/lb/docs/sm_lbs_978-3-540-48230-7_53
 |access-date=2020-06-14
 |language=en
}}
</ref>
|- style="background:#aaeeee"
| 4.21
| −268.94
| 100 kPa
| colspan="2" |[[Helium]]: Boiling point at atmospheric pressure (common cooling agent of low temperature physics; for reference)
|-
| 4.15
| −269.00
|
| Hg ([[Mercury (element)|Mercury]])<ref name="Kittel, Charles. 1996">
{{Cite book
 |last=Kittel |first=Charles
 |year=1996
 |title=Introduction to Solid State Physics  |edition=7th
 |publisher=Wiley |place=New York, NY
 |isbn=0-471-11181-3
 |oclc=32468930
}}
</ref>
| rowspan="2" |Metallic low-temperature superconductors
|-
| 1.09
| −272.06
|
| Ga ([[Gallium]])<ref name="Kittel, Charles. 1996"/>
|-
|}

== Properties ==
The "high-temperature" superconductor class has had many definitions.

The label high-{{mvar|T}}<sub>c</sub> should be reserved for materials with critical temperatures greater than the boiling point of [[liquid nitrogen]]. However, a number of materials{{snd}}including the original discovery and recently discovered pnictide superconductors{{snd}}have critical temperatures below {{cvt|77|K|C}} but nonetheless are commonly referred to in publications as high-{{mvar|T}}<sub>c</sub> class.<ref name=Norman2008>
{{cite journal
 |last=Norman  |first=Michael R.
 |year=2008
 |title=Trend: High-temperature superconductivity in the iron pnictides
 |journal=Physics
 |volume=1 |issue=21 |page=21
 |doi=10.1103/Physics.1.21 |doi-access=free |bibcode=2008PhyOJ...1...21N
}}
</ref><ref name=devereaux-stanford>
{{cite web
 |title=High-Temperature Superconductivity: The Cuprates
 |website=Devereaux group
 |publisher=Stanford University
 |url=http://www.stanford.edu/~tpd/research_hightc.html
 |access-date=March 30, 2012 |archive-url=https://web.archive.org/web/20100615231514/http://www.stanford.edu/~tpd/research_hightc.html
 |archive-date=June 15, 2010
}}
</ref>

A substance with a critical temperature above the boiling point of liquid nitrogen, together with a high critical magnetic field and critical current density (above which superconductivity is destroyed), would greatly benefit technological applications. In magnet applications, the high critical magnetic field may prove more valuable than the high {{mvar|T}}<sub>c</sub> itself. Some cuprates have an upper critical field of about 100&nbsp;tesla. However, cuprate materials are brittle ceramics that are expensive to manufacture and not easily turned into wires or other useful shapes. Furthermore, high-temperature superconductors do not form large, continuous superconducting domains, rather clusters of microdomains within which superconductivity occurs. They are therefore unsuitable for applications requiring actual superconductive currents, such as magnets for [[Nuclear magnetic resonance|magnetic resonance]] spectrometers.<ref>
{{cite journal
 |first1=S.   |last1=Graser   |first2=P. J.|last2=Hirschfeld
 |first3=T.   |last3=Kopp     |first4=R.   |last4=Gutser
 |first5=B. M.|last5=Andersen |first6=J.   |last6=Mannhart
 |date=June 27, 2010
 |title=How grain boundaries limit supercurrents in high-temperature superconductors
 |journal=[[Nature Physics]]
 |volume=6  |issue=8  |pages=609–614
 |doi=10.1038/nphys1687  |arxiv=0912.4191  |bibcode=2010NatPh...6..609G
|s2cid=118624779 }}
</ref> For a solution to this (powders), see [[Superconducting wire|HTS wire]].

There has been considerable debate regarding high-temperature superconductivity coexisting with [[magnetism|magnetic ordering]] in YBCO,<ref name=Sann2004>
{{cite journal
 | last1=Sanna   | first1=S.
 | last2=Allodi  | first2=G.
 | last3=Concas  | first3=G.
 | last4=Hillier | first4=A.
 | last5=Renzi   | first5=R.
 | year=2004
 | title=Nanoscopic coexistence of magnetism and superconductivity in YBa<sub>2</sub>Cu<sub>3</sub>O<sub>6+x</sub> detected by muon spin rotation
 | journal=[[Physical Review Letters]]
 | volume=93  | issue=20  | article-number=207001
 | arxiv=cond-mat/0403608   | bibcode=2004PhRvL..93t7001S
 | doi=10.1103/PhysRevLett.93.207001   | pmid=15600957   | s2cid=34327069
}}
</ref> [[iron-based superconductor]]s, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are [[Type-II superconductor]]s, which allow [[magnetic field]]s to penetrate their interior in [[quantum|quantized]] units of flux, meaning that much higher magnetic fields are required to suppress superconductivity. The layered structure also gives a directional dependence to the magnetic field response.

All known high-{{mvar|T}}<sub>c</sub> superconductors are Type-II superconductors. In contrast to [[Type-I superconductor]]s, which expel all magnetic fields due to the [[Meissner effect]], Type-II superconductors allow magnetic fields to penetrate their interior in quantized units of flux, creating "holes" or "tubes" of [[electrical conduction#Metals|normal metal]]lic regions in the superconducting bulk called [[Quantum vortex|vortices]]. Consequently, high-{{mvar|T}}<sub>c</sub> superconductors can sustain much higher magnetic fields.

=== Cuprates ===
{{Excerpt|Cuprate superconductor}}

=== Iron-based ===
{{Main|Iron-based superconductor}}
[[File:Phase diagram of the 122 family of ferro-pnictides.png|thumb|right|upright=1.4|[[Phase diagram]] for high-temperature superconductors based on iron<ref name="Kordyuk2012"/>]]

Iron-based superconductors contain layers of [[iron]] and a [[pnictogen]]{{snd}}such as [[arsenic]] or [[phosphorus]]{{snd}}, a [[chalcogen]], or a [[crystallogen]]. This is currently the family with the second highest critical temperature, behind the cuprates. Interest in their superconducting properties began in 2006 with the discovery of superconductivity in LaFePO at {{cvt|4|K|C}}<ref name=Hoso2006>{{cite journal |last1=Kamihara |first1=Y.   |last2=Hiramatsu |first2=H.
 |last3=Hirano   |first3=M.   |last4=Kawamura  |first4=R.
 |last5=Yanagi   |first5=H.   |last6=Kamiya    |first6=T.
 |last7=Hosono   |first7=H. |year=2006
 |title=Iron-based layered superconductor: LaOFeP
 |journal=[[Journal of the American Chemical Society]]
 |volume=128  |issue=31  |pages=10012–10013
 |doi=10.1021/ja063355c
 |pmid=16881620
|bibcode=2006JAChS.12810012K }}
</ref> and gained much greater attention in 2008 after the analogous material LaFeAs(O,F)<ref name=Kami2008>
{{cite journal
 |last1=Kamihara |first1=Y.
 |last2=Watanabe |first2=T.
 |last3=Hirano   |first3=M.
 |last4=Hosono   |first4=H.
 |year=2008
 |title=Iron-Based Layered Superconductor La[O<sub>1−x</sub>F<sub>x</sub>]FeAs (x=0.05–0.12) with {{mvar|T}}<sub>c</sub>&nbsp;=&nbsp;26&nbsp;K
 |journal=[[Journal of the American Chemical Society]]
 |volume=130 |issue=11 |pages=3296–3297
 |doi=10.1021/ja800073m
 |pmid=18293989
}}
</ref> was found to superconduct at up to {{cvt|43|K|C}} under pressure.<ref name=Taka2008>
{{cite journal
 |last1=Takahashi |first1=H.    |last2=Igawa    |first2=K.
 |last3=Arii      |first3=K.    |last4=Kamihara |first4=Y.
 |last5=Hirano    |first5=M.    |last6=Hosono   |first6=H.
 |s2cid=498756
 |year=2008
 |title=Superconductivity at 43&nbsp;K in an iron-based layered compound LaO1-<sub>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>
The highest critical temperatures in the iron-based superconductor family exist in thin films of FeSe,<ref name=Xue2012>
{{cite journal
 |last1=Wang  |first1=Qing-Yan    |last2=Li     |first2=Zhi 
 |last3=Zhang |first3=Wen-Hao     |last4=Zhang  |first4=Zuo-Cheng 
 |last5=Zhang |first5=Jin-Song    |last6=Li     |first6=Wei 
 |last7=Ding  |first7=Hao         |last8=Ou     |first8=Yun-Bo 
 |last9=Deng  |first9=Peng        |last10=Chang |first10=Kai 
 |last11=Wen  |first11=Jing       |last12=Song  |first12=Can-Li 
 |last13=He   |first13=Ke         |last14=Jia   |first14=Jin-Feng 
 |last15=Ji   |first15=Shuai-Hua  |last16=Wang  |first16=Ya-Yu
 |last17=Wang |first17=Li-Li      |last18=Chen  |first18=Xi 
 |last19=Ma   |first19=Xu-Cun     |last20=Xue   |first20=Qi-Kun
 |display-authors=6
 |year=2012
 |title=Interface-Induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO<sub>3</sub> 
 |journal=Chin. Phys. Lett.
 |volume=29   |issue=3   |article-number=037402
 |doi=10.1088/0256-307X/29/3/037402  |arxiv=1201.5694
 |bibcode=2012ChPhL..29c7402W   |s2cid=3858973 
}}
</ref><ref name=Liu2012>
{{cite journal
 |last1=Liu    |first1=Defa         |last2=Zhang |first2=Wenhao
 |last3=Mou    |first3=Daixiang     |last4=He    |first4=Junfeng
 |last5=Ou     |first5=Yun-Bo       |last6=Wang  |first6=Qing-Yan
 |last7=Li     |first7=Zhi          |last8=Wang  |first8=Lili
 |last9=Zhao   |first9=Lin          |last10=He   |first10=Shaolong
 |last11=Peng  |first11=Yingying    |last12=Liu  |first12=Xu
 |last13=Chen  |first13=Chaoyu      |last14=Yu   |first14=Li
 |last15=Liu   |first15=Guodong     |last16=Dong |first16=Xiaoli
 |last17=Zhang |first17=Jun         |last18=Chen |first18=Chuangtian
 |last19=Xu    |first19=Zuyan       |last20=Hu   |first20=Jiangping
 |last21=Chen  |first21=Xi          |last22=Ma   |first22=Xucun
 |last23=Xue   |first23=Qikun       |last24=Zhou |first24=X. J.
 |display-authors=6
 |year=2012
 |title=Electronic origin of high-temperature superconductivity in single-layer FeSe superconductor
 |journal=Nat. Commun.
 |volume=3  |issue=931  |page=931
 |doi=10.1038/ncomms1946  |pmid=22760630 |arxiv=1202.5849
 |bibcode=2012NatCo...3..931L  |s2cid=36598762
}}
</ref><ref name=He2013>
{{cite journal
 |last1=He    |first1=Shaolong      |last2=He     |first2=Junfeng
 |last3=Zhang |first3=Wenhao        |last4=Zhao   |first4=Lin
 |last5=Liu   |first5=Defa          |last6=Liu    |first6=Xu
 |last7=Mou   |first7=Daixiang      |last8=Ou     |first8=Yun-Bo
 |last9=Wang  |first9=Qing-Yan      |last10=Li    |first10=Zhi
 |last11=Wang |first11=Lili         |last12=Peng  |first12=Yingying
 |last13=Liu  |first13=Yan          |last14=Chen  |first14=Chaoyu
 |last15=Yu   |first15=Li           |last16=Liu   |first16=Guodong
 |last17=Dong |first17=Xiaoli       |last18=Zhang |first18=Jun
 |last19=Chen |first19=Chuangtian   |last20=Xu    |first20=Zuyan
 |last21=Chen |first21=Xi           |last22=Ma    |first22=Xucun
 |last23=Xue  |first23=Qikun        |last24=Zhou  |first24=X. J.
 |display-authors=6
 |year=2013
 |title=Phase diagram and electronic indication of high-temperature superconductivity at 65&nbsp;K in single-layer FeSe films
 |journal=Nat. Mater.
 |volume=12 |issue=7 |pages=605–610
 |doi=10.1038/NMAT3648 |pmid=23708329
 |arxiv=1207.6823 |bibcode=2013NatMa..12..605H
|s2cid=119185689 }}
</ref> where a critical temperature in excess of {{cvt|100|K|C}} was reported in 2014.<ref name=Ge2014>
{{cite journal
 |year=2014
 |title=Superconductivity in single-layer films of FeSe with a transition temperature above 100&nbsp;K
 |journal=Nature Materials
 |volume=1406  |issue=3  |pages=285–9
 |arxiv=1406.3435  |bibcode=2015NatMa..14..285G
 |pmid=25419814 |doi=10.1038/nmat4153
 |last1=Ge   |first1=J. F.
 |last2=Liu  |first2=Z. L.
 |last3=Liu  |first3=C.
 |last4=Gao  |first4=C. L.
 |last5=Qian |first5=D.
 |last6=Xue  |first6=Q. K.
 |last7=Liu  |first7=Y.
 |last8=Jia  |first8=J. F.
 |s2cid=119227626
 }}
</ref>

Since the original discoveries several families of iron-based superconductors have emerged:
* LnFeAs(O,F) or LnFeAsO<sub>1−x</sub> (Ln=lanthanide) with {{mvar|T}}<sub>c</sub> up to {{cvt|56|K|C}}, referred to as 1111 materials.<ref name=ren/> A [[fluoride]] variant of these materials was subsequently found with similar {{mvar|T}}<sub>c</sub> values.<ref name=Wu2008>
{{cite journal
 |last1=Wu    |first1=G.        |last2=Xie   |first2=Y. L.
 |last3=Chen  |first3=H.        |last4=Zhong |first4=M.
 |last5=Liu   |first5=R. H.     |last6=Shi   |first6=B. C.
 |last7=Li    |first7=Q. J.     |last8=Wang  |first8=X. F.
 |last9=Wu    |first9=T.        |last10=Yan  |first10=Y. J.
 |last11=Ying |first11=J. J.    |last12=Chen |first12=X. H.
 |display-authors=6
 |year=2009
 |title=Superconductivity at 56&nbsp;K in Samarium-doped SrFeAsF
 |journal=Journal of Physics: Condensed Matter
 |volume=21  |issue=3  |article-number=142203
 |arxiv=0811.0761  |doi=10.1088/0953-8984/21/14/142203
 |pmid=21825317  |bibcode=2009JPCM...21n2203W
 |s2cid=41728130
}}
</ref>
* (Ba,K)Fe<sub>2</sub>As<sub>2</sub> and related materials with pairs of iron-arsenide layers, referred to as 122 compounds. {{mvar|T}}<sub>c</sub> values range up to {{cvt|38|K|C}}.<ref name=Rotter2008>
{{cite journal
 |last1=Rotter   |first1=M.
 |last2=Tegel    |first2=M.
 |last3=Johrendt |first3=D.
 |year=2008
 |title=Superconductivity at 38&nbsp;K in the iron arsenide (Ba<sub>1−x</sub>K<sub>x</sub>)Fe<sub>2</sub>As<sub>2</sub>
 |journal=[[Physical Review Letters]]
 |volume=101   |issue=10   |article-number=107006
 |doi=10.1103/PhysRevLett.101.107006  |pmid=18851249  |arxiv=0805.4630
 |bibcode=2008PhRvL.101j7006R  |s2cid=25876149
}}
</ref><ref name=Sasmal2008>
{{cite journal
 |last1=Sasmal |first1=K.
 |last2=Lv     |first2=B.
 |last3=Lorenz |first3=B.
 |last4=Guloy  |first4=A. M.
 |last5=Chen   |first5=F.
 |last6=Xue    |first6=Y. Y.
 |last7=Chu    |first7=C. W.
 |year=2008
 |title=Superconducting Fe-based compounds (A<sub>1−x</sub>Sr<sub>x</sub>)Fe<sub>2</sub>As<sub>2</sub> with A=K and Cs with transition temperatures up to 37&nbsp;K
 |journal=[[Physical Review Letters]]
 |volume=101 |issue=10 |article-number=107007
 |doi=10.1103/PhysRevLett.101.107007  |pmid=18851250
 |bibcode=2008PhRvL.101j7007S  |arxiv=0806.1301
}}
</ref> These materials also superconduct when iron is replaced with [[cobalt]].
* LiFeAs and NaFeAs with {{mvar|T}}<sub>c</sub> up to around {{cvt|20|K|C}}. These materials superconduct close to stoichiometric composition and are referred to as 111 compounds.<ref name=Pitcher2008>
{{cite journal
 |last1=Pitcher    |first1=M. J.
 |last2=Parker     |first2=D. R.
 |last3=Adamson    |first3=P.
 |last4=Herkelrath |first4=S. J.
 |last5=Boothroyd  |first5=A. T.
 |last6=Ibberson   |first6=R. M.
 |last7=Brunelli   |first7=M.
 |last8=Clarke     |first8=S. J.
 |year=2008
 |title=Structure and superconductivity of LiFeAs
 |journal=[[Chemical Communications]]
 |volume=2008 |issue=45 |pages=5918–5920
 |doi=10.1039/b813153h |pmid=19030538 |arxiv=0807.2228 |s2cid=3258249
}}
</ref><ref name=Tapp2008>
{{cite journal
 |last1=Tapp |first1=Joshua H.
 |last2=Tang |first2=Zhongjia
 |last3=Lv |first3=Bing
 |last4=Sasmal |first4=Kalyan
 |last5=Lorenz |first5=Bernd
 |last6=Chu |first6=Paul C.W.
 |last7=Guloy |first7=Arnold M.
 |year=2008
 |title=LiFeAs: An intrinsic FeAs-based superconductor with {{mvar|T}}<sub>c</sub>=18&nbsp;K
 |journal=[[Physical Review B]]
 |volume=78  |issue=6  |article-number=060505
 |doi=10.1103/PhysRevB.78.060505 |bibcode=2008PhRvB..78f0505T |arxiv=0807.2274
 |s2cid = 118379012
}}
</ref><ref name=Parker2008>
{{cite journal
 |last1=Parker    |first1=D. R.
 |last2=Pitcher   |first2=M. J.
 |last3=Baker     |first3=P. J.
 |last4=Franke    |first4=I.
 |last5=Lancaster |first5=T.
 |last6=Blundell  |first6=S. J.
 |last7=Clarke    |first7=S. J.
 |year=2009
 |title=Structure, antiferromagnetism and superconductivity of the layered iron arsenide NaFeAs
 |journal=[[Chemical Communications]]
 |volume=2009  |issue=16  |pages=2189–2191
 |doi=10.1039/b818911k |pmid=19360189 |arxiv=0810.3214 |s2cid=45189652
}}
</ref>
* FeSe with small off-[[stoichiometry]] or [[tellurium]] doping.<ref name=Hsu2008>
{{cite journal
 |last1=Hsu   |first1=F. C.    |last2=Luo   |first2=J. Y.
 |last3=Yeh   |first3=K. W.    |last4=Chen  |first4=T. K.
 |last5=Huang |first5=T. W.    |last6=Wu    |first6=P. M.
 |last7=Lee   |first7=Y. C.    |last8=Huang |first8=Y. L.
 |last9=Chu   |first9=Y. Y.    |last10=Yan  |first10=D. C.
 |last11=Wu   |first11=M. K.   |display-authors=6
 |year=2008
 |title=Superconductivity in the PbO-type structure α-FeSe
 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
 |volume=105  |issue=38  |pages=14262–14264
 |doi=10.1073/pnas.0807325105  |pmid=18776050  |pmc=2531064
 |bibcode=2008PNAS..10514262H
|doi-access=free }}
</ref>
* LaFeSiH with {{mvar|T}}<sub>c</sub> around {{cvt|11|K|C}} in its stoichiometric composition.<ref name=Bernardini2018>
{{cite journal
 |last1=Bernardini   |first1=F.
 |last2=Garbarino    |first2=G.
 |last3=Sulpice      |first3=A.
 |last4=Núñnez-Regueiro   |first4=M.
 |last5=Gaudin       |first5=E.
 |last6=Chevalier    |first6=B.
 |last7=Measson    |first7=M.-A.
 |last8=Cano       |first8=A.
 |last9=Tencé    |first9=S.
|display-authors=1
 |year=2018
 |title=Iron-based superconductivity extended to the novel silicide LaFeSiH
 |journal=[[Physical Review B]]
 |volume=97   |issue=10   |article-number=100504
 |doi=10.1103/PhysRevB.97.100504
 |arxiv=1701.05010
|bibcode=2018PhRvB..97j0504B
 }}
</ref> This superconducting crystallogenide has oxide and fluoride variants LaFeSiO<sub>x</sub> and LaFeSiF<sub>x</sub>.<ref name=Hansen2022>
{{cite journal
 |last1=Hansen   |first1=M. F.
 |last2=x   |first2=x
|display-authors=1
 |year=2022
 |title=Superconductivity in the crystallogenide LaFeSiO1−δ with squeezed FeSi layers
 |journal=[[npj Quantum Materials]]
 |volume=7  |page=86
 |doi=10.1038/s41535-022-00493-z
 |arxiv=2206.11690
}}
</ref><ref name=Vaney2022>
{{cite journal
 |last1=Vaney   |first1=J. B.
 |last2=x   |first2=x
|display-authors=1
 |year=2022
 |title=Topotactic fluorination of intermetallics as an efficient route towards quantum materials
 |journal=[[Nature Communications]]
 |volume=13  
 |page=1462
 |doi=10.1038/s41467-022-29043-8
|pmid=35304455
 |pmc=8933527
 |bibcode=2022NatCo..13.1462V
 }}
</ref> 

Most undoped iron-based superconductors show a tetragonal-orthorhombic structural [[phase transition]] followed at lower temperature by magnetic ordering, similar to the cuprate superconductors.<ref name=Zhao2008>
{{cite journal
 |last1=Zhao       |first1=J.     |last2=Huang |first2=Q.
 |last3=de la Cruz |first3=C.     |last4=Li    |first4=S.
 |last5=Lynn       |first5=J. W.  |last6=Chen  |first6=Y.
 |last7=Green      |first7=M. A.  |last8=Chen  |first8=G. F.
 |last9=Li         |first9=G.     |last10=Li   |first10=Z.
 |last11=Luo       |first11=J. L. |last12=Wang |first12=N. L.
 |last13=Dai       |first13=P.    |display-authors=6
 |year=2008
 |title=Structural and magnetic phase diagram of CeFeAsO<sub>1−x</sub>F<sub>x</sub> and its relation to high-temperature superconductivity
 |journal=[[Nature Materials]]
 |volume=7  |issue=12  |pages=953–959
 |doi=10.1038/nmat2315 |pmid=18953342 |bibcode=2008NatMa...7..953Z
 |arxiv=0806.2528 |s2cid=25937023
}}
</ref> However, they are poor metals rather than Mott insulators and have five [[electronic band structure|band]]s at the Fermi surface rather than one.<ref name=Kordyuk2012>
{{Cite journal
 |last1      = Kordyuk |first1 = A. A.
 |year       = 2012
 |title      = Iron-based superconductors: Magnetism, superconductivity, and electronic structure (Review Article)
 |journal    = Low Temp. Phys.
 |volume     = 38   |issue = 9   |pages = 888–899
 |arxiv      = 1209.0140   |bibcode = 2012LTP....38..888K
 |doi        = 10.1063/1.4752092   |s2cid = 117139280
 |url        = http://www.imp.kiev.ua/~kord/papers/box/2012_LTP_Kordyuk.pdf
 |url-status = live
 |archive-url = https://web.archive.org/web/20150511190854/http://www.imp.kiev.ua/~kord/papers/box/2012_LTP_Kordyuk.pdf
 |archive-date = May 11, 2015  }}
</ref> 
The phase diagram emerging as the iron-arsenide layers are doped is remarkably similar, with the superconducting phase close to or overlapping the magnetic phase. Strong evidence that the {{mvar|T}}<sub>c</sub> value varies with the As–Fe–As bond angles has already emerged and shows that the optimal {{mvar|T}}<sub>c</sub> value is obtained with undistorted FeAs<sub>4</sub> tetrahedra.<ref name=Lee2008>
{{cite journal
 |last1=Lee |first1=Chul-Ho
 |last2=Iyo |first2=Akira
 |last3=Eisaki |first3=Hiroshi
 |last4=Kito |first4=Hijiri
 |last5=Teresa Fernandez-Diaz |first5=Maria
 |last6=Ito |first6=Toshimitsu
 |last7=Kihou |first7=Kunihiro
 |last8=Matsuhata |first8=Hirofumi
 |last9=Braden |first9=Markus
 |last10=Yamada |first10=Kazuyoshi
 |display-authors=6
 |year=2008
 |title=Effect of structural parameters on superconductivity in fluorine-free LnFeAsO<sub>1−y</sub> (Ln=La, Nd)
 |journal=[[Journal of the Physical Society of Japan]]
 |volume=77  |issue=8  |article-number=083704
 |doi=10.1143/JPSJ.77.083704  |bibcode=2008JPSJ...77h3704L  |arxiv=0806.3821
 |s2cid = 119112251
}}
</ref> The symmetry of the pairing wavefunction is still widely debated, but an extended ''s''-wave scenario is currently favoured.

=== Magnesium diboride ===
[[Magnesium diboride]] is occasionally referred to as a high-temperature superconductor<ref name=preuss>{{cite web|last=Preuss|first=Paul|title=A Most Unusual Superconductor and How It Works|url=http://www.lbl.gov/Science-Articles/Archive/MSD-superconductor-Cohen-Louie.html|publisher=Berkeley Lab|access-date=March 12, 2012|url-status=live|archive-url=https://web.archive.org/web/20120703001012/http://www.lbl.gov/Science-Articles/Archive/MSD-superconductor-Cohen-Louie.html|archive-date=July 3, 2012 }}</ref> because its {{mvar|T}}<sub>c</sub> value of {{cvt|39|K|C}} is above that historically expected for [[BCS theory|BCS]] superconductors. However, it is more generally regarded as the highest {{mvar|T}}<sub>c</sub> conventional superconductor, the increased {{mvar|T}}<sub>c</sub> resulting from two separate bands being present at the [[Fermi level]].

=== Carbon-based ===
In 1991 Hebard et al. discovered [[Fullerides|Fulleride]] superconductors,<ref name=Heba1991>
{{cite journal
 |last1=Hebard |first1=A. F.
 |last2=Rosseinsky |first2=M. J.
 |last3=Haddon |first3=R. C.
 |last4=Murphy |first4=D. W.
 |last5=Glarum |first5=S. H.
 |last6=Palstra |first6=T. T. M.
 |last7=Ramirez |first7=A. P.
 |last8=Kortan |first8=A. R.
 |year=1991
 |title=Superconductivity at 18&nbsp;K in potassium-doped C<sub>60</sub>
 |journal=[[Nature (journal)|Nature]]
 |volume=350  |issue=6319  |pages=600–601
 |doi=10.1038/350600a0 |bibcode=1991Natur.350..600H  |s2cid=4350005
 |url=https://pure.rug.nl/ws/files/14557724/1991NatureHebard.pdf
|hdl=11370/3709b8a7-6fc1-4b32-8842-ce9b5355b5e4|hdl-access=free}}
</ref> where alkali-metal atoms are intercalated into C<sub>60</sub> molecules.

In 2008 Ganin et al. demonstrated superconductivity at temperatures of up to {{cvt|38|K|C}} for Cs<sub>3</sub>C<sub>60</sub>.<ref name=ganin08>
{{cite journal
 |last1=Ganin |first1=A. Y.
 |last2=Takabayashi |first2=Y.
 |last3=Khimyak |first3=Y. Z.
 |last4=Margadonna |first4=S.
 |last5=Tamai |first5=A.
 |last6=Rosseinsky |first6=M. J.
 |last7=Prassides |first7=K.
 |year=2008
 |title=Bulk superconductivity at 38&nbsp;K in a molecular system
 |journal=[[Nature Materials]]
 |volume=7 |issue=5 |pages=367–71
 |doi=10.1038/nmat2179 |pmid=18425134 |bibcode=2008NatMa...7..367G
}}
</ref>

P-doped [[Graphane]] was proposed in 2010 to be capable of sustaining high-temperature superconductivity.<ref name=savini10>{{Cite journal |last1=Savini |first1=G. |last2=Ferrari |first2=A. C. |last3=Giustino |first3=F. |year=2010 |title=First-principles prediction of doped graphane as a high-temperature electron-phonon superconductor |journal=[[Physical Review Letters]] |volume=105 |issue=3 |article-number=037002 |arxiv=1002.0653 |bibcode=2010PhRvL.105c7002S |doi=10.1103/PhysRevLett.105.037002 |pmid=20867792|s2cid=118466816 }}</ref>

On 31st of December 2023 "Global Room-Temperature Superconductivity in Graphite" was published in the journal "Advanced Quantum Technologies" claiming to demonstrate superconductivity at room temperature and ambient pressure in [[Highly oriented pyrolytic graphite]] with dense arrays of nearly parallel line defects.<ref>{{cite journal | url=https://onlinelibrary.wiley.com/doi/10.1002/qute.202300230?ref=upstract.com | doi=10.1002/qute.202300230 | title=Global Room-Temperature Superconductivity in Graphite | date=2024 | last1=Kopelevich | first1=Yakov | last2=Torres | first2=José | last3=Da Silva | first3=Robson | last4=Oliveira | first4=Felipe | last5=Diamantini | first5=Maria Cristina | last6=Trugenberger | first6=Carlo | last7=Vinokur | first7=Valerii | journal=Advanced Quantum Technologies | volume=7 | issue=2 | arxiv=2208.00854 }}</ref>

=== Nickelates ===
In 1999, Anisimov et al. conjectured superconductivity in nickelates, proposing nickel oxides as direct analogs to the cuprate superconductors.<ref>
{{cite journal
 |last1=Anisimov  |first1=V. I.
 |last2=Bukhvalov |first2=D.
 |last3=Rice      |first3=T. M.
 |date=15 March 1999
 |title=Electronic structure of possible nickelate analogs to the cuprates
 |journal=Physical Review B
 |volume=59  |issue=12  |pages=7901–7906
 |bibcode=1999PhRvB..59.7901A  |doi=10.1103/PhysRevB.59.7901
}}
</ref> Superconductivity in an infinite-layer nickelate, Nd<sub>0.8</sub>Sr<sub>0.2</sub>NiO<sub>2</sub>, was reported at the end of 2019 with a superconducting transition temperature between {{cvt|9|and|15|K|C}}.<ref>
{{cite journal
 |last1=Li   |first1=D.
 |last2=Lee  |first2=K.
 |last3=Wang |first3=B. Y.
 |display-authors=etal
 |year=2019
 |title=Superconductivity in an infinite-layer nickelate
 |url= https://www.nature.com/articles/s41586-019-1496-5
 |journal= Nature
 |volume= 572 |issue= 7771
 |pages= 624–627
 |doi=  10.1038/s41586-019-1496-5
 |pmid= 31462797
 |bibcode= 2019Natur.572..624L
 |osti=1562463
 |s2cid= 201656573
}}
</ref><ref>
{{cite journal
 |last1=Botana     |first1=A. S.
 |last2=Bernardini |first2=F.
 |last3=Cano       |first3=A.
 |year=2021
 |title=Nickelate superconductors: an ongoing dialog between theory and experiments
 |journal=  Journal of Experimental and Theoretical Physics|volume= 132 |issue=4
 |pages= 618–627 |doi= 10.1134/S1063776121040026
 |arxiv=2012.02764
 |bibcode=2021JETP..132..618B
 |s2cid=255191342
}}
</ref> This superconducting phase is observed in oxygen-reduced thin films created by the pulsed laser deposition of Nd<sub>0.8</sub>Sr<sub>0.2</sub>NiO<sub>3</sub> onto SrTiO<sub>3</sub> substrates that is then reduced to Nd<sub>0.8</sub>Sr<sub>0.2</sub>NiO<sub>2</sub> via annealing the thin films at {{convert|260|-|280|C|K|order=flip}} in the presence of CaH<sub>2</sub>.<ref>
{{cite journal
 |last1= Wu        |first1= Xianxin     |last2= Di Sante |first2= Domenico
 |last3= Schwemmer |first3= Tilman      |last4= Hanke    |first4= Werner
 |last5= Hwang     |first5= Harold Y.   |last6= Raghu    |first6= Srinivas
 |last7= Thomale   |first7= Ronny
 |date= 24 February 2020
 |title=Robust d<sub>x<sup>2</sup>-y<sup>2</sup></sub>-wave superconductivity of infinite-layer nickelates
 |journal= Physical Review B
 |volume= 101 |issue= 6 |article-number= 060504
 |doi=10.1103/PhysRevB.101.060504 |arxiv= 1909.03015
 |bibcode= 2020PhRvB.101f0504W |s2cid= 202537199
 |url= https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.060504
}}
</ref> The superconducting phase is only observed in the oxygen reduced film and is not seen in oxygen reduced bulk material of the same stoichiometry, suggesting that the strain induced by the oxygen reduction of the Nd<sub>0.8</sub>Sr<sub>0.2</sub>NiO<sub>2</sub> thin film changes the phase space to allow for superconductivity.<ref>
{{cite journal
 |last1= Li |first1= Q.
 |last2= He |first2= C.
 |display-authors=etal
 |year=2020
 |title= Absence of supercondutivity in bulk Nd<sub>1−x</sub>Sr<sub>x</sub>NiO<sub>2</sub>
 |journal= Communications Materials
 |volume= 1 |issue= 1
 |page= 16
 |doi= 10.1038/s43246-020-0018-1 |arxiv= 1911.02420
 |bibcode= 2020CoMat...1...16L
 |doi-access= free  |s2cid= 208006588
}}
</ref>
Of important is further to extract access hydrogen from the reduction with CaH<sub>2</sub>, otherwise [[Topotactic transition|topotactic]] hydrogen may prevent superconductivity.
<ref>
{{cite journal
 |last1= Si |first1= L.
 |last2= Xiao |first2= W.
 |last3= Kaufmann |first3= J.
 |last4= Tomczak |first4= J. M.
 |last5= Lu |first5= X.
 |last6= Zhong |first6= Z.
 |last7= Held |first7= K.
 |display-authors=etal
 |year=2020
 |title= Topotactic Hydrogen in Nickelate Superconductors and Akin Infinite-Layer Oxides ABO<sub>2</sub>
 |url= https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.166402
 |journal= Physical Review Letters
 |volume= 124 |issue= 1
 |article-number= 166402 
 |doi= 10.1103/PhysRevLett.124.166402
 |pmid= 32383925
 |arxiv= 1911.06917  
 |bibcode= 2020PhRvL.124p6402S
 |s2cid= 208139397
 }}
</ref>

== Production ==
Liquid nitrogen can be produced relatively cheaply, even on-site. The higher temperatures additionally help to avoid some of the problems that arise at liquid helium temperatures, such as the formation of plugs of frozen air that can block cryogenic lines and cause unanticipated and potentially hazardous pressure buildup.<ref>{{cite web |title=Introduction to Liquid Helium |url=http://cryo.gsfc.nasa.gov/introduction/liquid_helium.html |work=Cryogenics and Fluid Branch |publisher=Goddard Space Flight Center, NASA}}</ref><ref>{{cite web |title=Section 4.1 'Air plug in the fill line' |url=http://www.2genterprises.com/cryo_manual_4.html |archive-url=https://web.archive.org/web/20090506030203/http://www.2genterprises.com/cryo_manual_4.html |archive-date=May 6, 2009 |access-date=9 October 2012 |work=Superconducting Rock Magnetometer Cryogenic System Manual |publisher=2G Enterprises}}</ref>

== Ongoing research ==
The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical [[condensed matter physics]]. The mechanism that causes the electrons in these crystals to form pairs is not known. Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, [[Bismuth strontium calcium copper oxide|BSCCO]]), making theoretical modelling difficult.

Improving the quality and variety of samples also gives rise to considerable research, both with the aim of improved characterisation of the physical properties of existing compounds, and synthesizing new materials, often with the hope of increasing {{mvar|T}}<sub>c</sub>. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable <ref>
{{cite journal
 |last1=Díez-Sierra |first1=Javier    |last2=López-Domínguez |first2=Pedro
 |last3=Rijckaert   |first3=Hannes    |last4=Rikel     |first4=Mark
 |last5=Hänisch     |first5=Jens     
 |display-authors=4
 |year=2021
 |title=All-chemical YBa2Cu3O7- $\delta$ coated conductors with preformed BaHfO3 and BaZrO3 nanocrystals on Ni5W technical substrate at the industrial scale
 |journal=Superconductor Science and Technology
 |volume=34 |issue=11 |page=114001
 |doi=10.1088/1361-6668/ac2495
 |bibcode=2021SuScT..34k4001D |url=https://iopscience.iop.org/article/10.1088/1361-6668/ac2495/meta
|hdl=1854/LU-8719549
|s2cid=237591103 |hdl-access=free}}
</ref> as well as in optimizing their properties in relation to [[Technological applications of superconductivity|applications]].<ref>
{{cite journal
 |last1=Díez-Sierra |first1=Javier    |last2=López-Domínguez |first2=Pedro
 |last3=Rijckaert   |first3=Hannes    |last4=Rikel     |first4=Mark
 |last5=Hänisch     |first5=Jens      |last6=Khan      |first6=Mukarram Zaman
 |last7=Falter      |first7=Martina   |last8=Bennewitz |first8=Jan
 |last9=Huhtinen    |first9=Hannu     |last10=Schäfer  |first10=Sebastian
 |last11=Müller     |first11=Robert   |last12=Schunk   |first12=Stephan Andreas
 |last13=Paturi     |first13=Petriina |last14=Bäcker   |first14=Michael
 |last15=De Buysser |first15=Klaartje |last16=Van Driessche |first16=Isabel
 |display-authors=6
 |year=2020
 |title=High critical current density and enhanced pinning in superconducting films of YBa2Cu3O7−δ nanocomposites with embedded BaZrO3, BaHfO3, BaTiO3, and SrZrO3 nanocrystals
 |journal=ACS Applied Nano Materials
 |volume=3 |issue=6 |pages=5542–5553
 |doi=10.1021/acsanm.0c00814
 |url=https://pubs.acs.org/doi/pdf/10.1021/acsanm.0c00814
|hdl=1854/LU-8661998|s2cid=219429094 |hdl-access=free}}
</ref>
[[Metallic hydrogen]] has been proposed as a room-temperature superconductor, some experimental observations have detected the occurrence of the [[Meissner effect]].<ref>{{cite journal|first1=Jorge E.|last1=Hirsch|first2=Frank|last2=Marsiglio|title=Meissner effect in nonstandard superconductors|date=January 2021|journal=Physica C: Superconductivity and Its Applications|arxiv=2101.01701|doi=10.1016/j.physc.2021.1353896|issn=0921-4534|volume=587|bibcode=2021PhyC..58753896H |s2cid=230523758 }}</ref><ref>{{Cite journal|url=https://pubs.acs.org/doi/full/10.1021/acs.jpcc.1c05831|title=Metallic Hydrogen: A Liquid Superconductor?|first1=Craig M.|last1=Tenney|first2=Zachary F.|last2=Croft|first3=Jeffrey M.|last3=McMahon|date=18 October 2021|journal=The Journal of Physical Chemistry C|volume=125|issue=42|pages=23349–23355|doi=10.1021/acs.jpcc.1c05831|arxiv=2107.00098|s2cid=182128526}}</ref> [[LK-99]], [[copper]]-[[Doping (semiconductor)|doped]] lead-apatite, has also been proposed as a room-temperature superconductor.

== Theoretical models ==
Multiple hypotheses attempt to account for HTS. 

=== Resonating valence bond theory ===
{{Main|Resonating valence bond theory}}
Spin fluctuation hypothesis<ref>{{cite journal |author=Mann |first=Adam |date=July 20, 2011 |title=High-temperature superconductivity at 25: Still in suspense |journal=Nature |volume=475 |issue=7356 |pages=280–2 |bibcode=2011Natur.475..280M |doi=10.1038/475280a |pmid=21776057 |s2cid=205066154 |doi-access=}}</ref> proposed that electron pairing in high-temperature superconductors is mediated by short-range spin waves known as [[Paramagnon|paramagnons]].<ref>{{citation |last=Pines |first=D. |title=The Gap Symmetry and Fluctuations in High-Tc Superconductors |date=2002 |volume=371 |pages=111–142 |series=NATO Science Series: B |contribution=The Spin Fluctuation Model for High Temperature Superconductivity: Progress and Prospects |place=New York |publisher=Kluwer Academic |doi=10.1007/0-306-47081-0_7 |isbn=978-0-306-45934-4}}</ref><ref>{{cite journal |author=Monthoux |first1=P. |last2=Balatsky |first2=A. V. |last3=Pines |first3=D. |name-list-style=amp |date=1991 |title=Toward a theory of high-temperature superconductivity in the antiferromagnetically correlated cuprate oxides |journal=Physical Review Letters |volume=67 |issue=24 |pages=3448–3451 |bibcode=1991PhRvL..67.3448M |doi=10.1103/PhysRevLett.67.3448 |pmid=10044736 |doi-access=free}}</ref>{{dubious|date=August 2016}} 

Gubser, Hartnoll, Herzog, and Horowitz proposed holographic superconductivity, which uses holographic duality or [[AdS/CFT correspondence]] theory as a possible explanation of high-temperature superconductivity in certain materials.<ref>Jan Zaanen, Yan Liu, Ya Sun K.Schalm (2015). ''Holographic Duality in Condensed Matter Physics''. Cambridge University Press, Cambridge.</ref> 

Weak coupling theory suggests superconductivity emerges from antiferromagnetic spin fluctuations in a doped system.<ref name="Mont1992">{{cite journal |last1=Monthoux |first1=P. |last2=Balatsky |first2=A. |last3=Pines |first3=D. |year=1992 |title=Weak-coupling theory of high-temperature superconductivity in the antiferromagnetically correlated copper oxides |journal=[[Physical Review B]] |volume=46  |issue=22  |pages=14803–14817 |doi=10.1103/PhysRevB.46.14803 |bibcode=1992PhRvB..4614803M |pmid=10003579}}</ref> It predicts that the pairing wave function of cuprate HTS should have a ''d''<sub>x</sub><sup>2</sup>-y<sup>2</sup> symmetry. Thus, determining whether the pairing wave function has ''d''-wave symmetry is essential to test the spin fluctuation mechanism. That is, if the HTS [[order parameter]] (a pairing wave function as in [[Ginzburg–Landau theory]]) does not have ''d''-wave symmetry, then a pairing mechanism related to spin fluctuations can be ruled out. (Similar arguments can be made for iron-based superconductors but the different material properties allow a different pairing symmetry.)

Interlayer coupling theory proposes that a layered structure consisting of BCS-type (''s''-wave symmetry) superconductors can explain superconductivity by itself.<ref name="Chak1993">
{{cite journal
 |last1=Chakravarty |first1=S.
 |last2=Sudbø |first2=A.
 |last3=Anderson |first3=P. W.
 |last4=Strong |first4=S.
 |year=1993
 |title=Interlayer Tunneling and Gap Anisotropy in High-Temperature Superconductors
 |journal=[[Science (journal)|Science]]
 |volume=261  |issue=5119  |pages=337–340
 |doi=10.1126/science.261.5119.337 |pmid=17836845
 |bibcode=1993Sci...261..337C |s2cid=41404478
}}
</ref> By introducing an additional tunnelling interaction between layers, this model explained the anisotropic symmetry of the order parameter as well as the emergence of HTS.  

In order to resolve this question, experiments such as [[photoemission spectroscopy]], [[Nuclear magnetic resonance|NMR]], [[specific heat capacity|specific heat]] measurements, were conducted. The results remain ambiguous, with some reports supporting ''d'' symmetry, with others supporting ''s'' symmetry. 

Such explanations assume that superconductive properties can be treated by [[mean-field theory]]. It also does not consider that in addition to the superconductive gap, the [[pseudogap]] must be explained. The cuprate layers are insulating, and the superconductors are doped with interlayer impurities to make them metallic. 

The transition temperature can be maximized by varying the [[dopant]] concentration. The simplest example is La<sub>2</sub>CuO<sub>4</sub>, which consists of alternating CuO<sub>2</sub> and LaO layers that are insulating when pure. When 8% of the La is replaced by Sr, the latter acts as a dopant, contributing holes to the CuO<sub>2</sub> layers, and making the sample metallic. The Sr impurities also act as electronic bridges, enabling interlayer coupling. Proceeding from this picture, some theories argue that the pairing interaction is with [[phonons]], as in conventional superconductors with [[Cooper pairs]]. While the undoped materials are antiferromagnetic, even a few percent of impurity dopants introduce a smaller pseudogap in the CuO<sub>2</sub> planes that is also caused by phonons. The gap decreases with increasing charge carriers, and as it nears the superconductive gap, the latter reaches its maximum. The transition temperature is then argued to be due to the percolating behaviour of the carriers, which follow zig-zag percolative paths, largely in metallic domains in the CuO<sub>2</sub> planes, until blocked by charge density wave [[domain walls]], where they use dopant bridges to cross over to a metallic domain of an adjacent CuO<sub>2</sub> plane. The transition temperature maxima are reached when the host lattice has weak bond-bending forces, which produce strong electron–phonon interactions at the interlayer dopants.<ref name="pnas">
{{cite journal
 |last=Phillips |first=J.
 |date=2010
 |title=Percolative theories of strongly disordered ceramic high-temperature superconductors
 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
 |volume=43 |issue=4 |pages=1307–10
 |pmid=20080578 |pmc=2824359 |doi=10.1073/pnas.0913002107
 |bibcode=2010PNAS..107.1307P
|doi-access=free
 }}
</ref>

=== D symmetry in YBCO ===
[[File:Meissner effect p1390048.jpg|thumb|Small magnet levitating above a high-temperature superconductor cooled by [[liquid nitrogen]]: this is a case of [[Meissner effect]].]]

An experiment based on flux quantization of a three-grain ring of [[Yttrium barium copper oxide|YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub> (YBCO)]] was proposed to test the symmetry of the order parameter in the HTS. The symmetry of the order parameter could best be probed at the junction interface as the Cooper pairs tunnel across a [[Josephson junction]] or weak link.<ref name=Gesh1987>{{cite journal |last1=Geshkenbein |first1=V. |last2=Larkin |first2=A. |last3=Barone |first3=A. |year=1987 |title=Vortices with half magnetic flux quanta in ''heavy-fermion'' superconductors |journal=[[Physical Review B]] |volume=36  |issue=1  |pages=235–238 |doi=10.1103/PhysRevB.36.235 |bibcode=1987PhRvB..36..235G |pmid=9942041}}</ref> It was expected that a half-integer flux, that is, a spontaneous magnetization could only occur for a junction of ''d'' symmetry superconductors. But, even if the junction experiment is the strongest method to determine the symmetry of the HTS order parameter, the results have been ambiguous. [[John R. Kirtley]] and C. C. Tsuei thought that the ambiguous results came from the defects inside the HTS, leading them to an experiment where both clean limit (no defects) and dirty limit (maximal defects) were considered simultaneously.<ref name=Kirt1995>
{{cite journal
 |last1=Kirtley |first1=J. R.
 |last2=Tsuei |first2=C. C.
 |last3=Sun |first3=J. Z.
 |last4=Chi |first4=C. C.
 |last5=Yu-Jahnes |first5=Lock See
 |last6=Gupta |first6=A.
 |last7=Rupp |first7=M.
 |last8=Ketchen |first8=M. B.
 |year=1995
 |title=Symmetry of the order parameter in the high-{{mvar|T}}<sub>c</sub> superconductor YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7−δ</sub>
 |journal=[[Nature (journal)|Nature]]
 |volume=373  |issue=6511  |pages=225–228
 |doi=10.1038/373225a0 |bibcode=1995Natur.373..225K |s2cid=4237450
}}
</ref> Spontaneous magnetization was clearly observed in YBCO, which supported the ''d'' symmetry of the order parameter in YBCO. But, since YBCO is [[orthorhombic]], it might inherently have an admixture of ''s'' symmetry. By tuning their technique, they found an admixture of ''s'' symmetry in YBCO within about 3%.<ref name=Kirt2006>{{cite journal |last1=Kirtley |first1=J. R. |last2=Tsuei |first2=C. C. |last3=Ariando |first3=A. |last4=Verwijs |first4=C. J. M. |last5=Harkema |first5=S. |last6=Hilgenkamp |first6=H.
 |year=2006 |title=Angle-resolved phase-sensitive determination of the in-plane gap symmetry in YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7−δ</sub>
 |journal=[[Nature Physics]]
 |volume=2  |issue=3   |pages=190–194
 |doi=10.1038/nphys215 |bibcode=2006NatPh...2..190K |s2cid=118447968
|url=https://ris.utwente.nl/ws/files/6613933/angle.pdf }}
</ref> Also, they found a pure ''d''<sub>x<sup>2</sup>−y<sup>2</sup></sub> order parameter symmetry in tetragonal Tl<sub>2</sub>Ba<sub>2</sub>CuO<sub>6</sub>.<ref name=Tsue1997>
{{cite journal |last1=Tsuei   |first1=C. C. |last2=Kirtley |first2=J. R.
 |last3=Ren     |first3=Z. F.
 |last4=Wang    |first4=J. H.
 |last5=Raffy   |first5=H.
 |last6=Li      |first6=Z. Z.
 |year=1997
 |title=Pure ''d''<sub>x<sup>2</sup>−y<sup>2</sup></sub> order-parameter symmetry in the tetragonal superconductor Tl<sub>2</sub>Ba<sub>2</sub>CuO<sub>6+δ</sub>
 |journal=[[Nature (journal)|Nature]]
 |volume=387  |issue=6632  |pages=481–483
 |doi=10.1038/387481a0 |bibcode=1997Natur.387..481T |s2cid=4314494
}}
</ref>

=== Spin-fluctuation mechanism ===
The lack of exact theoretical computations on such strongly interacting electron systems has complicated attempts to validate spin-fluctuation. However, most theoretical calculations, including phenomenological and diagrammatic approaches, converge on magnetic fluctuations as the pairing mechanism. 

==== Qualitative explanation ====
In a superconductor, the flow of electrons cannot be resolved into individual electrons, but instead consists of pairs of bound electrons, called Cooper pairs. In conventional superconductors, these pairs are formed when an electron moving through the material distorts the surrounding crystal lattice, which attracts another electron and forms a bound pair. This is sometimes called the "water bed" effect. Each Cooper pair requires a certain minimum energy to be displaced, and if the thermal fluctuations in the crystal lattice are smaller than this energy the pair can flow without dissipating energy. Electron flow without resistance is superconductivity.

In a high-{{mvar|T}}<sub>c</sub> superconductor, the mechanism is extremely similar to a conventional superconductor, except that phonons play virtually no role, replaced by spin-density waves. Just as all known conventional superconductors are strong phonon systems, all known high-{{mvar|T}}<sub>c</sub> superconductors are strong spin-density wave systems, within close vicinity of a magnetic transition to, for example, an antiferromagnet. When an electron moves in a high-{{mvar|T}}<sub>c</sub> superconductor, its spin creates a spin-density wave around it. This spin-density wave in turn causes a nearby electron to fall into the spin depression created by the first electron (water-bed). When the system temperature is lowered, more spin density waves and Cooper pairs are created, eventually leading to superconductivity. High-{{mvar|T}}<sub>c</sub> systems are magnetic systems due to the Coulomb interaction, creating a strong Coulomb repulsion between electrons. This repulsion prevents pairing of the Cooper pairs on the same lattice site. Instead, pairing occurs at near-neighbor lattice sites. This is the so-called ''d''-wave pairing, where the pairing state has a node (zero) at the origin.

== Examples ==
{{Main|List of superconductors}}
Examples of high-{{mvar|T}}<sub>c</sub> cuprate superconductors include [[YBCO]] and [[BSCCO]], which are the most known materials that achieve superconductivity above the boiling point of liquid nitrogen.

{| class="wikitable" style="text-align:center "
|+ Temperatures of most practical superconductors and coolants, at ordinary pressures
! <!--  style="width:7%;"|   --> Transition temperature
! <!--  style="width:15%;"|  --> Item
! <!--  style="width:30%;"|  --> Material type
|-
| style="background:#ddddff" | {{cvt|195|K|C}}
| style="background:#ddddff" | [[Dry ice|Dry ice (Carbon dioxide)]]{{snd}}[[Sublimation (phase transition)|sublimation]]
| style="background:#ddddff" | Coolant
|-
| style="background:#ddddff" | {{cvt|184|K|C}}
| style="background:#ddddff" |[[Lowest temperature recorded on Earth]]
| style="background:#ddddff" | Coolant
|-
| {{cvt|110|K|C}}
| [[BSCCO]]
| style="background:blue;" rowspan="2" | [[Cuprate superconductor|<span style="color:white;">Cuprate superconductors</span>]]
|-
| {{cvt|93|K|C}}
| [[YBCO]] 
|-
| style="background:#ddddff" |{{cvt|77|K|C}}
| style="background:#ddddff" |[[liquid nitrogen|Nitrogen]]{{snd}}Boiling
| style="background:#ddddff" | Coolant
|-
| {{cvt|55|K|C}}
| SmFeAs(O,F)
| style="background:orange" rowspan="3"|[[Iron-based superconductor]]s
|-
| {{cvt|41|K|C}}
| CeFeAs(O,F)
|-
| {{cvt|26|K|C}}
| LaFeAs(O,F)
|-
| {{cvt|18|K|C}}
| [[Niobium-tin|Nb<sub>3</sub>Sn]]
| style="background:#c0c0c0;" rowspan="1"|Metallic low-temperature superconductors
|-
| style="background:#ddddff" |3K (−270&nbsp;°C)
| style="background:#ddddff" |[[liquid helium|Helium]]{{snd}}boiling
| style="background:#ddddff" | Coolant
|-
| {{cvt|3|K|C}}
| Hg ([[Mercury (element)|mercury]]: the first discovered superconductor)
| style="background:#c0c0c0;"|Metallic low-temperature superconductors
|}

== See also ==

* {{annotated link|Flux pumping}}
* {{annotated link|Macroscopic quantum phenomena}}
* {{annotated link|Mixed conduction}}
* {{annotated link|SQUID}}
* {{annotated link|Superconducting wire}}
* {{annotated link|Superconductor classification}}
* {{annotated link|Superstripes}}
* {{annotated link|Technological applications of superconductivity}}

== References ==

{{refs}}

== External links ==

* {{cite web |url=https://www.youtube.com/watch?v=c3asSdngzLs | archive-url=https://ghostarchive.org/varchive/youtube/20211211/c3asSdngzLs| archive-date=2021-12-11 | url-status=live|title=Video of a magnet floating on a HTSC|website=[[YouTube]]| date=31 July 2006}}{{cbignore}}
* {{cite web |url=http://www.suptech.com/tech_faq.htm |title=High-Temperature Superconductor Technologies|archive-url=https://web.archive.org/web/20080325021825/http://www.suptech.com/tech_faq.htm|archive-date=25 March 2008}}
* {{cite book |url=https://www.springer.com/materials/book/978-1-4020-0810-8 |title=High-Temperature Superconductivity in Cuprates |year=2002 |publisher=Springer |isbn=1-4020-0810-4}}
* {{cite magazine |url=https://www.scientificamerican.com/article/iron-exposed-as-high-temp-superconductor/ |title=New LaOFeAs HTS |magazine=Scientific American |first=Charles Q. |last=Choi |date=June 1, 2008 |access-date=November 2, 2022 }}
* {{cite journal |title=Pseudogap from ARPES experiment: Three gaps in cuprates and topological superconductivity (Review Article) |type=Review |year=2015 |doi=10.1063/1.4919371 |arxiv=1501.04154|last1=Kordyuk |first1=A. A. |journal=Low Temperature Physics |volume=41 |issue=5 |pages=319–341 |bibcode=2015LTP....41..319K |s2cid=56392827 }}
* {{Cite journal |title=Thanks to a bit of diamond smashing, practical room-temperature superconductivity could be close to reality |url=https://www.science.org/content/article/thanks-bit-diamond-smashing-practical-room-temperature-superconductivity-could-be-close |first=Robert F. |last=Service |journal=[[Science (journal)|Science]] |publisher=[[American Association for the Advancement of Science|AAAS]] |language=en}}

{{Use American English|date=January 2019}}
{{Use dmy dates|date=March 2020}}
{{emerging technologies|topics=yes|robotics=yes|manufacture=yes|materials=yes}}
{{Superconductivity}}

{{Authority control}}

[[Category:High-temperature superconductors]]
[[Category:Correlated electrons]]
[[Category:Unsolved problems in physics]]