Editing Unconventional superconductor

{{Short description|Superconductive materials not explained by existing established theories}}
{{Use American English|date=January 2019}}
{{Use mdy dates|date=January 2019}}

'''Unconventional superconductors''' are materials that display [[superconductivity]] which is not explained by the usual [[BCS theory]] or its extension, the [[Eliashberg theory]]. The pairing in unconventional superconductors may originate from some other mechanism than the electron–phonon interaction.<ref>{{Cite journal |last=Hirsch |first=J. E. |last2=Maple |first2=M. B. |last3=Marsiglio |first3=F. |date=2015-07-15 |title=Superconducting materials classes: Introduction and overview |url=https://www.sciencedirect.com/science/article/pii/S0921453415000933 |journal=Physica C: Superconductivity and its Applications |series=Superconducting Materials: Conventional, Unconventional and Undetermined |volume=514 |pages=1–8 |doi=10.1016/j.physc.2015.03.002 |issn=0921-4534|arxiv=1504.03318 }}</ref> Alternatively, a superconductor is unconventional if the superconducting [[order parameter]] transforms according to a non-trivial [[irreducible representation]] of the [[point group]] or [[space group]] of the system.<ref name="c718">{{cite book |last=Mineev |first=V.P. |title=Introduction to Unconventional Superconductivity |last2=Samokhin |first2=K |date=1999-09-21 |publisher=CRC Press |isbn=978-90-5699-209-5 |publication-place=Amsterdam |pages=vii, 20}}</ref> Per definition, superconductors that break additional symmetries to ''U'' (1) symmetry are known as unconventional superconductors.<ref>{{Cite journal |last=Sigrist |first=Manfred |last2=Ueda |first2=Kazuo |date=1991-04-01 |title=Phenomenological theory of unconventional superconductivity |url=https://link.aps.org/doi/10.1103/RevModPhys.63.239 |journal=Reviews of Modern Physics |language=en |volume=63 |issue=2 |pages=239–311 |doi=10.1103/RevModPhys.63.239 |issn=0034-6861}}</ref>  

== History ==

The superconducting properties of  CeCu<sub>2</sub>Si<sub>2</sub>, a type of
[[heavy fermion material]], were reported in 1979 by [[Frank Steglich]].<ref>{{cite journal |doi=10.1103/PhysRevLett.43.1892|title=Superconductivity in the Presence of Strong Pauli Paramagnetism: CeCu2Si2 |year=1979 |last1=Steglich |first1=F. |first2=J. |journal=Physical Review Letters |volume=43 |pages=1892–1896 |last2=Aarts |last3=Bredl |first3=C.D. |last4=Lieke |first4=W. |last5=Meschede |first5=D. |last6=Franz |first6=W. |last7=Schäfer |first7=H. |bibcode=1979PhRvL..43.1892S |issue=25 |hdl=1887/81461 |s2cid=123497750 |hdl-access=free }}</ref> For a long time it was believed that CeCu<sub>2</sub>Si<sub>2</sub> was a singlet d-wave superconductor, but since the mid-2010s, this notion has been strongly contested.<ref>{{Cite journal |last1=Kittaka|first1=Shunichiro|last2=Aoki|first2=Yuya|last3=Shimura|first3=Yasuyuki|last4=Sakakibara|first4=Toshiro|last5=Seiro|first5=Silvia|last6=Geibel|first6=Christoph|last7=Steglich|first7=Frank|last8=Ikeda|first8=Hiroaki|last9=Machida|first9=Kazushige|date=2014-02-12|title=Multiband Superconductivity with Unexpected Deficiency of Nodal Quasiparticles in CeCu<sub>2</sub>Si<sub>2</sub>|journal=Physical Review Letters|volume=112|issue=6|pages=067002|doi=10.1103/PhysRevLett.112.067002|bibcode=2014PhRvL.112f7002K|pmid=24580704|arxiv=1307.3499|s2cid=13367098 }}</ref> In  the early eighties, many more unconventional, [[heavy fermion]] [[Superconductivity|superconductors]] were discovered, including UBe<sub>13</sub>,<ref>{{cite journal |doi=10.1103/PhysRevLett.50.1595|title=UBe_{13}: An Unconventional Actinide Superconductor|year=1983|last1=Ott|first1=H. R.|last2=Rudigier|first2=H.|last3=Fisk|first3=Z.|last4=Smith|first4=J.|journal=Physical Review Letters|volume=50|issue=20|pages=1595–1598|bibcode=1983PhRvL..50.1595O|url=https://escholarship.org/uc/item/18w6w653 }}</ref> [[UPt3|UPt<sub>3</sub>]]<ref>{{cite journal|doi=10.1103/PhysRevLett.52.679|title=Possibility of Coexistence of Bulk Superconductivity and Spin Fluctuations in UPt<sub>3</sub>|year=1984|last1=Stewart|first1=G. R.|first2=Z.|first3=J. O.|first4=J. L.|journal=Physical Review Letters|volume=52|pages=679–682|last2=Fisk|last3=Willis|last4=Smith|bibcode=1984PhRvL..52..679S|issue=8|s2cid=73591098 |url=http://www.escholarship.org/uc/item/6px8s7q3}}</ref> and URu<sub>2</sub>Si<sub>2</sub>.<ref>{{cite journal|doi=10.1103/PhysRevLett.55.2727|pmid=10032222|title=Superconducting and Magnetic Transitions in the Heavy-Fermion System URu_{2}Si_{2}|year=1985|last1=Palstra|first1=T. T. M.|last2=Menovsky|first2=A. A.|last3=Berg|first3=J. van den|last4=Dirkmaat|first4=A. J.|last5=Kes|first5=P. H.|last6=Nieuwenhuys|first6=G. J.|last7=Mydosh|first7=J. A.|journal=Physical Review Letters|volume=55|issue=24|pages=2727–2730|bibcode=1985PhRvL..55.2727P|url=https://www.rug.nl/research/portal/en/publications/superconducting-and-magnetic-transitions-in-the-heavyfermion-system-uru2si2(ade9b7b6-f4eb-4973-bfbe-7837626183c0).html}}</ref> In each of these materials, the anisotropic nature of the pairing was implicated by the power-law dependence of the [[nuclear magnetic resonance]] (NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt<sub>3</sub> was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.<ref>{{cite journal|doi=10.1103/PhysRevLett.56.1078|title=Anisotropy of Transverse Sound in the Heavy-Fermion Superconductor UPt<sub>3</sub>
|year=1986|first4=D.|last1=Shivaram|last4=Hinks|first1=B. S.|first2=Y. H.|first3=T.F.|journal=Physical Review Letters|volume=56|pages=1078–1081|last2=Jeong|last3=Rosenbaum|pmid=10032562|bibcode=1986PhRvL..56.1078S|issue=10|url=https://authors.library.caltech.edu/47038/1/PhysRevLett.56.1078.pdf}}</ref>

The first unconventional triplet superconductor, organic material (TMTSF)<sub>2</sub>PF<sub>6</sub>, was discovered by [[Denis Jerome]], [[Klaus Bechgaard]] and coworkers in 1980 (TMTSF = Tetramethyltetraselenafulvalenium, see [[Fulvalene]]).<ref>{{cite journal |doi=10.1051/jphyslet:0198000410409500 |title=Superconductivity in a synthetic organic conductor (TMTSF)2PF 6 |year=1980 |last1=Jérome |first1=D. |first2=A. |first3=M. |first4=K. |journal=Journal de Physique Lettres |volume=41 |pages=95 |last2=Mazaud |last3=Ribault |last4=Bechgaard |issue=4 |url=https://hal.archives-ouvertes.fr/jpa-00231730/file/ajp-jphyslet_1980_41_4_95_0.pdf }}</ref> Experimental works by [[Paul Chaikin]]'s and Michael Naughton's groups as well as theoretical analysis of their data by [[Andrei Lebed]] have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)<sub>2</sub>X (X=PF<sub>6</sub>, ClO<sub>4</sub>, etc.) organic materials.<ref>{{cite journal |doi=10.1103/PhysRevLett.46.852|title=Zero-Pressure Organic Superconductor: Di-(Tetramethyltetraselenafulvalenium)-Perchlorate [(TMTSF)2ClO4]|year=1981|last1=Bechgaard|first1=Klaus|first2=Claus S.|journal=Physical Review Letters|volume=46|pages=852|last2=Carneiro|last3=Olsen|first3=Malte|last4=Rasmussen|first4=Finn|last5=Jacobsen|first5=Claus|bibcode=1981PhRvL..46..852B|issue=13|url=http://orbit.dtu.dk/files/4927636/Bech.pdf}}</ref>

High-temperature singlet d-wave superconductivity was discovered by [[J.G. Bednorz]] and [[Karl Alexander Müller|K.A. Müller]] in 1986, who also discovered that the [[lanthanum]]-based [[cuprate superconductor|cuprate]] [[perovskite]] material LaBaCuO<sub>4</sub>  develops superconductivity  at a critical temperature (''T''<sub>c</sub>) of approximately 35&nbsp;[[kelvin|K]] (-238 degrees [[Celsius]]). This was well above the highest critical temperature known at the time (''T''<sub>c</sub> = 23&nbsp;K), and thus the new family of materials was called [[High-temperature superconductivity|high-temperature superconductors]]. Bednorz and Müller received the [[Nobel Prize in Physics]] for this discovery in 1987. Since then, many other [[High-temperature superconductivity|high-temperature superconductors]] have been synthesized.

LSCO (La<sub>2−''x''</sub>Sr<sub>''x''</sub>CuO<sub>4</sub>) was discovered the same year (1986). Soon after, in January 1987, [[yttrium barium copper oxide]] (YBCO) was discovered to have a ''T''<sub>c</sub> of 90&nbsp;K, the first material to achieve superconductivity above the boiling point of [[liquid nitrogen]] (77&nbsp;K).<ref>{{cite journal |title=Superconductivity at 93 K in a new mixed-phase Yb-Ba-Cu-O compound system at ambient pressure |author=K. M. Wu |journal=Phys. Rev. Lett. |volume=58 |issue=9 |year=1987 |pages=908–910 |doi=10.1103/PhysRevLett.58.908|pmid=10035069 |bibcode=1987PhRvL..58..908W |display-authors=etal |doi-access=free }}</ref> This was highly significant from the point of view of the [[technological applications of superconductivity]] because liquid nitrogen is far less expensive than [[liquid helium]], which is required to cool [[conventional superconductor]]s down to their critical temperature. In 1988 [[bismuth strontium calcium copper oxide]] (BSCCO) with ''T''<sub>c</sub> up to 107&nbsp;K,<ref>{{cite journal|title = A New High-''T''<sub>c</sub> Oxide Superconductor without a Rare Earth Element|author1=H. Maeda |author2=Y. Tanaka |author3=M. Fukutumi |author4=T. Asano  |name-list-style=amp |journal=Jpn. J. Appl. Phys. |volume=27 |issue=2 |pages=L209–L210 |year=1988 |doi=10.1143/JJAP.27.L209 |bibcode=1988JaJAP..27L.209M |doi-access=free }}</ref> and [[thallium barium calcium copper oxide]] (TBCCO) (T=thallium) with ''T''<sub>c</sub> of 125&nbsp;K were discovered. The current record critical temperature is about ''T''<sub>c</sub>&nbsp;= 133&nbsp;K (−140&nbsp;°C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless, at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.

On the other hand, other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as [[strontium ruthenate|strontium ruthenate Sr<sub>2</sub>RuO<sub>4</sub>]], but that, like high-temperature superconductors, are unconventional in other ways. (For example, the origin of the attractive force leading to the formation of [[Cooper pair]]s may be different from the one postulated in [[BCS theory]].) In addition to this, superconductors that have unusually high values of ''T''<sub>c</sub> but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of [[conventional superconductor]]s (this is suspected of [[magnesium diboride]], MgB<sub>2</sub>, with ''T''<sub>c</sub> = 39&nbsp;K). Others could display more unconventional features.

In 2008 a new class that does not include copper (layered [[oxypnictide]] superconductors), for example LaOFeAs, was discovered.<ref name = "Superconductivity">{{cite journal |title = Superconductivity at 43K in an iron-based layered compound LaO<sub>1−''x''</sub>F<sub>''x''</sub>FeAs | author1 = Hiroki Takahashi | author2 = Kazumi Igawa | author3 = Kazunobu Arii | author4 = Yoichi Kamihara | author5 = Masahiro Hirano|author6= Hideo Hosono | journal = Nature|volume = 453|pages = 376–378|year = 2008|doi = 10.1038/nature06972|pmid = 18432191|issue = 7193|bibcode=2008Natur.453..376T|s2cid = 498756}}</ref><ref>{{cite web |url=http://www.sciam.com/article.cfm?id=iron-exposed-as-high-temp-superconductor |title=A New Iron Age: New class of superconductor may help pin down mysterious physics |first=Charles Q. |last=Choi |date=June 1, 2008 |work=Scientific American |access-date=2009-10-29}}</ref><ref>{{Cite web |url=https://www.sciencedaily.com/releases/2008/05/080528140242.htm |title=New High-Temperature Superconductors Are Iron-based With Unusual Magnetic Properties |website=ScienceDaily |date=June 1, 2008 |author=National Institute of Standards and Technology}}</ref> An oxypnictide of [[samarium]] seemed to have a ''T''<sub>c</sub> of about 43&nbsp;K, which was higher than predicted by BCS theory.<ref>{{cite journal | last1=Chen | first1=X. H. | last2=Wu | first2=T. | last3=Wu | first3=G. | last4=Liu | first4=R. H. | last5=Chen | first5=H. | last6=Fang | first6=D. F. | title=Superconductivity at 43 K in SmFeAsO<sub>1−x</sub>F<sub>X</sub> | journal=Nature | year=2008 | volume=453 | issue=7196 | pages=761–762 | doi=10.1038/nature07045 | pmid=18500328 | arxiv=0803.3603 | bibcode=2008Natur.453..761C | s2cid=205213713 }}</ref> Tests at up to 45&nbsp;[[tesla (unit)|T]]<ref>[http://www.planetanalog.com/news/showArticle.jhtml?articleID=208401297 High-temp superconductors pave way for 'supermagnets']{{Dead link|date=July 2018 |bot=InternetArchiveBot |fix-attempted=no }}</ref><ref>{{cite journal |doi=10.1038/nature07058|title=Very High Field Two-band Superconductivity in LaFeAsO0.89F0.11 at very high magnetic fields|year=2008|last1=Hunte|first1=F.|first2=J.|first3=A.|first4=D. C.|first5=R.|first6=A. S.|first7=M. A.|first8=B. C.|first9=D. K.|last10=Mandrus|first10=D.|journal=Nature|volume=453|pages=903–5|pmid=18509332|last2=Jaroszynski|last3=Gurevich|last4=Larbalestier|last5=Jin|last6=Sefat|last7=McGuire|last8=Sales|last9=Christen|issue=7197|bibcode = 2008Natur.453..903H |display-authors=8|arxiv=0804.0485|s2cid=115211939 }}</ref> suggested the upper critical field of LaFeAsO<sub>0.89</sub>F<sub>0.11</sub> to be around 64&nbsp;T. Some other [[iron-based superconductor]]s do not contain oxygen.

{{As of|2009}}, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>''x''</sub>), at 138&nbsp;K and is held by a cuprate-perovskite material,<ref>{{cite journal |author1 = P. Dai|author2 = B. C. Chakoumakos|author3 = G. F. Sun|author4 = K. W. Wong |author5 = Y. Xin |author6 = D. F. Lu|title = Synthesis and neutron powder diffraction study of the superconductor HgBa<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>8+δ</sub> by Tl substitution|journal = Physica C|volume = 243|year = 1995|pages = 201–206|doi = 10.1016/0921-4534(94)02461-8|issue = 3–4|bibcode=1995PhyC..243..201D }}</ref> possibly 164 K under high pressure.<ref>{{cite journal |author1=L. Gao |author2=Y. Y. Xue |author3=F. Chen |author4=Q. Xiong |author5=R. L. Meng |author6=D. Ramirez |author7=C. W. Chu |author8=J. H. Eggert |author9=H. K. Mao  |name-list-style=amp |title = Superconductivity up to 164 K in HgBa<sub>2</sub>Ca<sub>m-1</sub>Cu<sub>m</sub>O<sub>2m+2+δ</sub> (m=1, 2, and 3) under quasihydrostatic pressures|journal = Phys. Rev. B|volume = 50|year = 1994|pages = 4260–4263|doi = 10.1103/PhysRevB.50.4260|issue = 6|pmid=9976724 |bibcode=1994PhRvB..50.4260G }}</ref>

Other unconventional superconductors not based on cuprate structure have too been found.<ref name = "Superconductivity" /> Some have unusually high values of the [[critical temperature]], ''T''<sub>c</sub>, and hence they are sometimes also called high-temperature superconductors.

=== Graphene ===

In 2017, [[Scanning tunneling microscope|scanning tunneling microscopy]] and spectroscopy experiments on [[graphene]] proximitized to the electron-doped (non-chiral) ''d''-wave superconductor Pr<sub>2−''x''</sub>Ce<sub>''x''</sub>CuO<sub>4</sub> (PCCO) revealed evidence for an unconventional superconducting density of states induced in graphene.<ref>{{Cite journal |last1=Di Bernardo|first1=A.|last2=Millo|first2=O.|last3=Barbone|first3=M.|last4=Alpern|first4=H.|last5=Kalcheim|first5=Y.|last6=Sassi|first6=U.|last7=Ott|first7=A. K.|last8=Fazio|first8=D. De|last9=Yoon|first9=D.|date=2017-01-19|title=p-wave triggered superconductivity in single-layer graphene on an electron-doped oxide superconductor|journal=Nature Communications|language=en|volume=8|doi=10.1038/ncomms14024|issn=2041-1723|page=14024|arxiv=1702.01572|bibcode=2017NatCo...814024D|pmid=28102222|pmc=5253682 }}</ref> Publications in March 2018 provided evidence for unconventional [[Bilayer graphene#Superconductivity in twisted bilayer graphene|superconducting properties of a graphene bilayer]] where [[Twistronics|one layer was offset]] by a "magic angle" of 1.1° relative to the other.<ref>{{Cite journal |last=Gibney|first=Elizabeth|author-link=Elizabeth Gibney|date=5 March 2018|title=Surprise graphene discovery could unlock secrets of superconductivity|department=News|journal=Nature|volume=555|issue=7695|pages=151&ndash;2|quote=Physicists now report that arranging two layers of atom-thick graphene so that the pattern of their carbon atoms is offset by an angle of 1.1º makes the material a superconductor.|bibcode=2018Natur.555..151G|doi=10.1038/d41586-018-02773-w|pmid=29517044|doi-access=free }}</ref>

==Ongoing research==
While the mechanism responsible for conventional superconductivity is well described by the BCS theory,<ref>{{Cite journal |last=Bardeen |first=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |date=1957-04-01 |title=Microscopic Theory of Superconductivity |url=https://link.aps.org/doi/10.1103/PhysRev.106.162 |journal=Physical Review |language=en |volume=106 |issue=1 |pages=162–164 |doi=10.1103/PhysRev.106.162 |issn=0031-899X}}</ref><ref>{{Cite journal |last=Bardeen |first=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |date=1957-12-01 |title=Theory of Superconductivity |url=https://link.aps.org/doi/10.1103/PhysRev.108.1175 |journal=Physical Review |language=en |volume=108 |issue=5 |pages=1175–1204 |doi=10.1103/PhysRev.108.1175 |issn=0031-899X}}</ref> the mechanism for unconventional superconductivity is still unknown. After more than twenty years of intense research, the origin of high-temperature superconductivity is still not clear, being one of the [[List of unsolved problems in physics#Condensed matter physics|major unsolved problems]] of theoretical [[condensed matter physics]]. It appears that unlike conventional superconductivity driven by ''electron-phonon'' attraction, genuine ''electronic'' mechanisms (such as  antiferromagnetic correlations) are at play. Moreover, d-wave pairing, rather than s-wave, is significant.

One goal of much research is [[room-temperature superconductor|room-temperature superconductivity]].<ref>{{cite book|author = A. Mourachkine|title = Room-Temperature Superconductivity|publisher = Cambridge International Science Publishing |arxiv=cond-mat/0606187|year = 2004|isbn=1-904602-27-4|bibcode=2006cond.mat..6187M}}</ref>

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, [[BSCCO]]), making theoretical modeling difficult.

==Possible mechanisms==
<!-- huge overlap with High-temperature_superconductivity#Possible_mechanism -->
The most controversial topic in condensed matter physics has been the mechanism for high-''T''<sub>c</sub> superconductivity (HTS). There have been two representative theories on the HTS :  (See also [[Resonating valence bond theory]] )

===Weak-coupling theory===
Firstly, it has been suggested that the HTS emerges by antiferromagnetic spin fluctuation in a doped system.<ref>{{cite journal|author=P. Monthoux|journal=Phys. Rev. B|volume=46|year=1992|title=Weak-coupling theory of high-temperature superconductivity in the antiferromagnetically correlated copper oxides|doi=10.1103/PhysRevB.46.14803|issue=22|bibcode=1992PhRvB..4614803M|last2=Balatsky|first2=A.|last3=Pines|first3=D.|pages=14803–14817|pmid=10003579|display-authors=etal}}</ref> According to this [[weak-coupling theory]], the pairing wave function of the HTS should have a ''d''<sub>''x''<sup>2</sup>−''y''<sup>2</sup></sub> symmetry. Thus, whether the symmetry of the pairing wave function is the ''d'' symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation. That is, if the HTS order parameter (pairing wave function) does not have ''d'' symmetry, then a pairing mechanism related to spin fluctuation can be ruled out. The ''tunnel experiment'' (see below) seems to detect ''d'' symmetry in some HTS.

===Interlayer coupling model===
Secondly, there is the [[interlayer coupling model]], according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself.<ref>{{cite journal|author=S. Chakravarty|journal=Science|volume=261|pages=337–40|year=1993|title=Interlayer Tunneling and Gap Anisotropy in High-Temperature Superconductors|doi=10.1126/science.261.5119.337|pmid=17836845|issue=5119|bibcode=1993Sci...261..337C|last2=Sudbo|first2=A.|last3=Anderson|first3=P. W.|last4=Strong|first4=S.|s2cid=41404478|display-authors=etal}}</ref> By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS.{{citation needed|date=June 2020}}

===Superexchange===
Promising experimental results from various researchers in September 2022, including [[Weijiong Chen]], [[J. C. Séamus Davis|J.C. Séamus Davis]] and [[H. Eisiaki]] revealed that [[superexchange]] of electrons is possibly the most probable reason for high-temperature superconductivity.<ref>{{Cite journal |last1=O’Mahony |first1=Shane M. |last2=Ren |first2=Wangping |last3=Chen |first3=Weijiong |last4=Chong |first4=Yi Xue |last5=Liu |first5=Xiaolong |last6=Eisaki |first6=H. |last7=Uchida |first7=S. |last8=Hamidian |first8=M. H. |last9=Davis |first9=J. C. Séamus |date=2022-09-13 |title=On the electron pairing mechanism of copper-oxide high temperature superconductivity |journal=Proceedings of the National Academy of Sciences |language=en |volume=119 |issue=37 |pages=e2207449119 |doi=10.1073/pnas.2207449119 |issn=0027-8424 |pmc=9477408 |pmid=36067325|arxiv=2108.03655 |bibcode=2022PNAS..11907449O }}</ref><ref>{{Cite magazine |last=Wood |first=Charlie |title=The High-Temperature Superconductivity Mystery Is Finally Solved |language=en-US |magazine=Wired |url=https://www.quantamagazine.org/high-temperature-superconductivity-understood-at-last-20220921/ |access-date=2022-12-26 |issn=1059-1028}}</ref>

==Previous studies on the symmetry of the HTS order parameter==
The symmetry of the HTS order parameter has been studied in [[nuclear magnetic resonance]] measurements and, more recently, by [[ARPES|angle-resolved photoemission]] and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS.

NMR measurements of the resonance frequency on [[YBCO]] indicated that electrons in the copper oxide superconductors are paired in [[singlet state|spin-singlet]] states. This indication came from the behavior of the [[Knight shift]], the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it.

Also, by measuring the ''penetration depth'', the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/''k''<sub>B</sub>''T''). In that case, the penetration depth also varies exponentially with temperature ''T''. If there are nodes in the energy gap as in the ''d'' symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially ''d''<sub>''x''<sup>2</sup>-''y''<sup>2</sup></sub> then the penetration depth should vary linearly with ''T'' at low temperatures. This technique is increasingly being used to study superconductors and is limited in application largely by the quality of available single crystals.

[[Photoemission spectroscopy]] also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the [[angle-resolved photoemission spectroscopy]] (ARPES), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the ''d'' symmetry or not.

==Junction experiment supporting the ''d-wave'' symmetry==

There was a clever experimental design to overcome the muddy situation. An experiment based on pair tunneling and flux quantization in a three-grain ring of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub> (YBCO) was designed to test the symmetry of the order parameter in YBCO.
<ref name="Tsuei1994">{{cite journal|author=C. C. Tsuei|journal=Phys. Rev. Lett.|volume=73|year=1994|title=Pairing Symmetry and Flux Quantization in a Tricrystal Ring of Superconductin YBa2Cu3O7- delta|doi=10.1103/PHYSREVLETT.73.593|bibcode=1994PhRvL..73..593T|last2=Kirtley|first2=J. R.|last3=Chi|first3=C. C.|last4=Yu-Jahnes|first4=Lock See|last5=Gupta|first5=A.|last6=Shaw|first6=T.|last7=Sun|first7=J. Z.
|last8=Ketchen|first8=M. B.|issue=4|pages=593–596|pmid=10057486|display-authors=etal}}</ref> Such a ring consists of three YBCO crystals with specific orientations consistent with the d-wave pairing symmetry to give rise to a spontaneously generated half-integer quantum vortex at the tricrystal meeting point. Furthermore, the possibility that junction interfaces can be in the clean limit (no defects) or with maximum zig-zag disorder was taken into account in this tricrystal experiment.<ref name="Tsuei1994" />
A proposal of studying vortices with half magnetic flux quanta in heavy-fermion superconductors in three polycrystalline configurations was reported in 1987 by V. B. Geshkenbein, A. Larkin and A. Barone in 1987.<ref>{{cite journal|author=V. B. Geshkenbein|journal=Phys. Rev. B|volume=36|issue=1|pages=235–238|year=1987|title=Vortices with half magnetic flux quanta in ''heavy-fermion'' superconductors|doi=10.1103/PhysRevB.36.235|bibcode=1987PhRvB..36..235G|last2=Larkin|first2=A.|last3=Barone|first3=A.|display-authors=etal|pmid=9942041}}</ref>

In the first tricrystal pairing symmetry experiment,<ref name="Tsuei1994" /> the spontaneous magnetization of half flux quantum was clearly observed in YBCO, which convincingly supported the ''d-wave'' symmetry of the order parameter in YBCO. Because YBCO is [[orthorhombic]], it might inherently have an admixture of s-wave symmetry. So, by tuning their technique further, it was found that there was an admixture of s-wave symmetry in YBCO within about 3%.<ref>{{cite journal|author=J. R. Kirtley|journal=Nat. Phys.|volume=2|page=190|year=2006|title=Angle-resolved phase-sensitive determination of the in-plane gap symmetry in YBa2Cu3O7-delta|doi=10.1038/nphys215|issue=3|bibcode=2006NatPh...2..190K|last2=Tsuei|first2=C. C.|last3=Ariando|first3=A.|last4=Verwijs|first4=C. J. M.|last5=Harkema|first5=S.|last6=Hilgenkamp|first6=H.|s2cid=118447968|display-authors=etal}}</ref> Also, it was demonstrated by Tsuei, Kirtley et al. that there was a pure ''d''<sub>''x''<sup>2</sup>-''y''<sup>2</sup></sub> order parameter symmetry in the [[tetragonal]] Tl<sub>2</sub>Ba<sub>2</sub>CuO<sub>6</sub>.<ref>{{cite journal|author=C. C. Tsuei|journal=Nature|volume=387|page=481|year=1997|title=Pure dx2 – y2 order-parameter symmetry in the tetragonal superconductor TI2Ba2CuO6+delta|doi=10.1038/387481a0|issue=6632|bibcode=1997Natur.387..481T|last2=Kirtley|first2=J. R.|last3=Ren|first3=Z. F.|last4=Wang|first4=J. H.|last5=Raffy|first5=H.|last6=Li|first6=Z. Z.|s2cid=4314494|display-authors=etal}}</ref>

==References==
{{reflist|30em}}
{{Superconductivity}}

[[Category:Superconductors]]