electron quadruplets
The condensate of electron quadruplets is a proposed state of matter in which Cooper pairs do not exhibit long-range order, but electron quadruplets do. Such states emerge in systems with multiple broken symmetries due to the partial melting of the underlying low-temperature order, which destroys the condensates of Cooper pairs but preserves the condensates formed by pairs of preformed fermion pairs.{{Cite journal |last1=Babaev |first1=Egor |last2=Sudbø |first2=Asle |last3=Ashcroft |first3=N. W. |date=October 2004 |title=A superconductor to superfluid phase transition in liquid metallic hydrogen |url=https://www.nature.com/articles/nature02910 |journal=Nature |language=en |volume=431 |issue=7009 |pages=666–668 |doi=10.1038/nature02910 |pmid=15470422 |arxiv=cond-mat/0410408 |bibcode=2004Natur.431..666B |issn=1476-4687}}{{cite journal |last1=Smiseth |first1=J. |last2=Smørgrav |first2=E. |last3=Babaev |first3=E. |last4=Sudbø |first4=A. |title=Field- and temperature-induced topological phase transitions in the three-dimensional N -component London superconductor |journal=Physical Review B |date=6 June 2005 |volume=71 |issue=21 |page=214509 |doi=10.1103/PhysRevB.71.214509|arxiv=cond-mat/0411761 |bibcode=2005PhRvB..71u4509S }} One example of the proposed electron quadruplet condensates is
charge-4e {{Cite journal |last1=Berg |first1=Erez |last2=Fradkin |first2=Eduardo |last3=Kivelson |first3=Steven A. |date=November 2009 |title=Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors |url=https://www.nature.com/articles/nphys1389 |journal=Nature Physics |language=en |volume=5 |issue=11 |pages=830–833 |doi=10.1038/nphys1389 |arxiv=0904.1230 |bibcode=2009NatPh...5..830B |issn=1745-2481}} {{cite journal |last1=Radzihovsky |first1=Leo |last2=Vishwanath |first2=Ashvin |title=Quantum Liquid Crystals in an Imbalanced Fermi Gas: Fluctuations and Fractional Vortices in Larkin-Ovchinnikov States |journal=Physical Review Letters |date=2 July 2009 |volume=103 |issue=1 |pages=010404 |doi=10.1103/PhysRevLett.103.010404 |pmid=19659128 |arxiv=0812.3945 |bibcode=2009PhRvL.103a0404R }}Another example is "quartic metal" phase {{Cite journal |last1=Bojesen |first1=Troels Arnfred |last2=Babaev |first2=Egor |last3=Sudbø |first3=Asle |date=2013-12-30 |title=Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems |url=https://link.aps.org/doi/10.1103/PhysRevB.88.220511 |journal=Physical Review B |volume=88 |issue=22 |pages=220511 |doi=10.1103/PhysRevB.88.220511|arxiv=1306.2313 |bibcode=2013PhRvB..88v0511B }}{{Cite journal |last1=Bojesen |first1=Troels Arnfred |last2=Babaev |first2=Egor |last3=Sudbø |first3=Asle |date=2014-03-11 |title=Phase transitions and anomalous normal state in superconductors with broken time-reversal symmetry |url=https://link.aps.org/doi/10.1103/PhysRevB.89.104509 |journal=Physical Review B |volume=89 |issue=10 |pages=104509 |doi=10.1103/PhysRevB.89.104509|arxiv=1401.5802 |bibcode=2014PhRvB..89j4509B }} is distinct from those superconductors explained by the standard BCS theory; rather than expelling magnetic field lines as in the Meissner effect, it generates them, a spontaneous Nernst effect that indicates the breaking of time-reversal symmetry.{{Cite journal|last1=Grinenko|first1=Vadim|last2=Weston|first2=Daniel|last3=Caglieris|first3=Federico|last4=Wuttke|first4=Christoph|last5=Hess|first5=Christian|last6=Gottschall|first6=Tino|last7=Maccari|first7=Ilaria|last8=Gorbunov|first8=Denis|last9=Zherlitsyn|first9=Sergei|last10=Wosnitza|first10=Jochen|last11=Rydh|first11=Andreas|last12=Kihou |first12=Kunihiro
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|last22=Babaev |first22=Egor |author-link22=Egor Babaev |date=2021-10-18|title=State with spontaneously broken time-reversal symmetry above the superconducting phase transition|url=https://www.nature.com/articles/s41567-021-01350-9|journal=Nature Physics|volume=17|issue=11|language=en|pages=1254–1259|arxiv=2103.17190|bibcode=2021arXiv210317190G|doi=10.1038/s41567-021-01350-9|s2cid=235732434|issn=1745-2481}}
Related states can form in pair-density-wave systems.{{cite journal |last1=Agterberg |first1=D. F. |last2=Tsunetsugu |first2=H. |title=Dislocations and vortices in pair-density-wave superconductors |journal=Nature Physics |date=August 2008 |volume=4 |issue=8 |pages=639–642 |doi=10.1038/nphys999|arxiv=0902.0805 |bibcode=2008NatPh...4..639A }} In systems with a greater number of broken symmetries, theoretical studies have demonstrated the existence of charge-6e and more complex orders.{{cite journal |last1=Herland |first1=Egil V. |last2=Babaev |first2=Egor |last3=Sudbø |first3=Asle |title=Phase transitions in a three dimensional U ( 1 ) × U ( 1 ) lattice London superconductor: Metallic superfluid and charge- 4 e superconducting states |journal=Physical Review B |date=8 October 2010 |volume=82 |issue=13 |page=134511 |doi=10.1103/PhysRevB.82.134511|arxiv=1006.3311 |bibcode=2010PhRvB..82m4511H }}{{cite journal |last1=Agterberg |first1=D. F. |last2=Geracie |first2=M. |last3=Tsunetsugu |first3=H. |title=Conventional and charge-six superfluids from melting hexagonal Fulde-Ferrell-Larkin-Ovchinnikov phases in two dimensions |journal=Physical Review B |date=26 July 2011 |volume=84 |issue=1 |page=014513 |doi=10.1103/PhysRevB.84.014513|arxiv=1106.1685 |bibcode=2011PhRvB..84a4513A }}
After the theoretical possibility was raised, observations consistent with electron quadrupling were published using hole-doped Ba1-xKxFe2As2 in 2021,{{Cite web|date=2021-11-03|title=Superconductor reveals new state of matter involving pairs of Cooper pairs|url=https://physicsworld.com/superconductor-reveals-new-state-of-matter-involving-pairs-of-cooper-pairs/|access-date=2021-11-06|website=Physics World|language=en-GB}} with claims of charge-4e state reported in mesoscopic samples of CsV3Sb5 soon after, in early 2022.{{Cite journal |title= Charge-4𝑒 and Charge-6𝑒 Flux Quantization and Higher Charge Superconductivity in Kagome Superconductor Ring Devices |url= https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.021025 |journal=Physical Review X |volume=89 |issue=14 |pages=021025 |doi= 10.1103/PhysRevX.14.021025 |arxiv= 2201.10352 |last1= Ge |first1= Jun |last2= Wang |first2= Pinyuan |last3= Xing |first3= Ying |last4= Yin |first4= Qiangwei |last5= Wang |first5= Anqi |last6= Shen |first6= Jie |last7= Lei |first7= Hechang |last8= Wang |first8= Ziqiang |last9= Wang |first9= Jian |date= 2022 }}