Distrontium ruthenate: Difference between revisions

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'''Distrontium ruthenate''' is an [[oxide]] of [[strontium]] and [[ruthenium]] with the [[chemical formula]] Sr₂RuO₄. It was the first reported [[Perovskite (structure)|perovskite]] [[superconductor]] that did not contain [[copper]].<ref name=maeno1994 /><ref name=yanoff2000>{{cite book|last=Yanoff|first=Brian|title=Temperature dependence of the penetration depth in the unconventional superconductor Sr₂RuO₄|year=2000|publisher=University of Illinois at Urbana-Champaign|url=http://groups.mrl.uiuc.edu/dvh/theses/yanoff.pdf}}</ref> Strontium ruthenate is structurally very similar to the [[High-temperature superconductivity#Cuprates|high-temperature cuprate]] superconductors,<ref name=wooten>{{cite web|last=Wooten|first=Rachel|title=Strontium Ruthenate|url=https://docs.google.com/viewer?a=v&q=cache:DgnknpjYbx4J:sces.phys.utk.edu/~dagotto/condensed/HW2_2008/Strontium_Ruthenate.ppt+&hl=en&gl=us&pid=bl&srcid=ADGEESjZ7iZGRQSADAb7Z1s_9eAna1xiWVss132uKFgZzdWLT0aMoimFedsvEYqudjD3jQQnZj0ttTougqs1felMdAWruV20EbFHDcoyabxp8gHZE7bmi1WI28B0Y5qLzU42RqJuuJwO&sig=AHIEtbTQVVf6y8oDl63wDTUkXKH9NrNEug&pli=1|publisher=University of Tennessee-Knoxville|access-date=16 April 2012}}</ref> and in particular, is almost identical to the [[lanthanum]] doped superconductor (La, Sr)₂CuO₄.<ref name=maeno2001>{{cite journal|author1=Yoshiteru Maeno|author2=Maurice Rice |author3=Manfred Sigrist |title=The intriguing superconductivity of Strontium Ruthenate|journal=Physics Today|year=2001|volume=54|issue=1|doi=10.1063/1.1349611|url=http://www.physics.mcmaster.ca/~imai/PhysicsToday_2001.pdf|access-date=16 April 2012|bibcode = 2001PhT....54a..42M|pages=42 |doi-access=free}}</ref> However, the [[critical temperature|transition temperature]] for the superconducting phase transition is 0.93 [[Kelvin|K]] (about 1.5 [[Kelvin|K]] for the best sample), which is much lower than the corresponding value for cuprates.<ref name=maeno1994Rev>{{cite journal|author1=Yoshiteru Maeno|author2doi=H10.1103/RevModPhys.84.253|title=Structure, HashimotoPhysical Properties, and Applications of SrRuO₃ Thin Films |titleyear=Superconductivity2012 in|last1=Koster a|first1=Gertjan layered|last2=Klein perovskite|first2=Lior without|last3=Siemons copper|journalfirst3=NatureWolter |yearlast4=1994Rijnders |volumefirst4=372Guus |pageslast5=532–534Dodge |doifirst5=10J.1038/372532a0 Steven |bibcodelast6=Eom |first6=Chang-Beom 1994Natur|last7=Blank |first7=Dave H.372 A. |last8=Beasley |first8=Malcolm R.532M |journal=Reviews of Modern Physics |volume=84 |issue=65061 |s2cidpages=4303356253–298 |display-authorsbibcode=etal2012RvMP...84..253K |url=https://research.utwente.nl/en/publications/structure-physical-properties-and-applications-of-srruo3-thin-films(1e2b4b92-c67d-4854-af92-6aab57227116).html }}</ref>

High-quality crystals of strontium ruthenate are synthesized using a [[floating zone method]] in a controlled atmosphere with ruthenium as flux. The perovskite structure can be deduced based on [[powder diffraction|powder x-ray diffraction]] measurements. Strontium ruthenate behaves as a conventional [[Fermi liquid]] at temperatures below 25 K.<ref name=yanoff2000 />

==Superconductivity==

Superconductivity in SRO was first observed by Yoshiteru Maeno andet his group in 1994 when they were looking for high temperature superconductors with structures similar to the cupratesal. Unlike the cupratescuprate superconductors, SRO displays superconductivity even in the absence of [[Doping (semiconductor)|doping]].<ref name=wooten Rev/> The superconducting [[order parameter]] in SRO has been shown to exhibitexhibits signatures of [[time-reversal symmetry]] breaking,<ref name=kapitulnik2009>{{cite journal|author1=Aharon Kapitulnik|author2=Jing Xia |author3=Elizabeth Schemm Alexander Palevski |title=Polar Kerr effect as probe for time-reversal symmetry breaking in unconventional superconductors|journal=New Journal of Physics|date=May 2009|volume=11|doi=10.1088/1367-2630/11/5/055060|arxiv = 0906.2845 |bibcode = 2009NJPh...11e5060K|issue=5|pages=055060 |s2cid=43924082}}</ref> and hence, it can be classified as an [[unconventional superconductor]].

Sr₂RuO₄ is believed to be a fairly two-dimensional system, with superconductivity occurring primarily on the Ru-O plane. The electronic structure of Sr₂RuO₄ is characterized by three bands derived from the Ru t_2g 4d orbitals, namely, α, β and γ bands, of which the first is hole-like while the other two are electron-like. Among them, the γ band arises mainly from the d_xy orbital, while the α and β bands emerge from the hybridization of d_xz and d_yz orbitals. Due to the two-dimensionality of Sr₂RuO₄, its [[Fermi surface]] consists of three nearly two-dimensional sheets with little dispersion along the crystalline c-axis and that the compound is nearly magnetic.<ref>{{cite journal | last1=Mazin | first1=I. I. | last2=Singh | first2=David J. | title=Ferromagnetic Spin Fluctuation Induced Superconductivity in Sr₂RuO₄ | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=79 | issue=4 | date=1997-07-28 | issn=0031-9007 | doi=10.1103/physrevlett.79.733 | pages=733–736| arxiv=cond-mat/9703068 | bibcode=1997PhRvL..79..733M | s2cid=119434737 }}</ref>

Early proposals have suggested that superconductivity is dominant in the γ band. In particular, the candidate [[chiral p-wave]] order parameter in the momentum space exhibits k-dependence phase winding which is characteristic of time-reversal symmetry breaking. This peculiar single-band superconducting order is expected to give rise to appreciable spontaneous supercurrent at the edge of the sample. Such an effect is closely associated with the topology of the Hamiltonian describing Sr₂RuO₄ in the superconducting state, which is characterized by a nonzero [[Chern number]]. However, scanning probes have so far failed to detect expected time-reversal symmetry breaking fields generated by the supercurrent, off by orders of magnitude.<ref name=Hicks2010>{{cite journal|last=Hicks|first=Clifford W.|title=Limits on superconductivity-related magnetization in Sr₂RuO₄ and PrOs₄Sb₁₂ from scanning SQUID microscopy|journal=Physical Review B|year=2010|volume=81|issue=21|pages=214501|doi=10.1103/PhysRevB.81.214501|arxiv = 1003.2189 |bibcode = 2010PhRvB..81u4501H |s2cid=26608198|display-authors=etal}}</ref> This has led some to speculate that superconductivity arises dominantly from the α and β bands instead.<ref name=Raghu2010>{{cite journal|last1=Raghu|first1=S.|last2=Marini|first2=Aharon|last3=Pankratov|first3=Steve|last4=Rubio|first4=Angel |title=Hidden Quasi-One-Dimensional Superconductivity in Sr₂RuO₄|url=http://prl.aps.org/abstract/PRL/v105/i13/e136401|journal= Physical Review Letters|volume=105|issue=13| page=136401|year=2010|arxiv = 1003.3927 |bibcode = 2010PhRvL.105b6401B |doi = 10.1103/PhysRevLett.105.026401|pmid=20867720|s2cid=26117260}}</ref> Such a two-band superconductor, although having k-dependence phase winding in its order parameters on the two relevant bands, is topologically trivial with the two bands featuring opposite Chern numbers. Therefore, it could possibly give a much reduced if not completely cancelled supercurrent at the edge. However, this naive reasoning was later found not to be entirely correct: the magnitude of edge current is not directly related to the topological property of the chiral state.<ref>{{cite journal | last1=Huang | first1=Wen | last2=Lederer | first2=Samuel | last3=Taylor | first3=Edward | last4=Kallin | first4=Catherine|author4-link= Catherine Kallin | title=Nontopological nature of the edge current in a chiralp-wave superconductor | journal=Physical Review B | volume=91 | issue=9 | date=2015-03-12 | issn=1098-0121 | doi=10.1103/physrevb.91.094507 | page=094507| arxiv=1412.4592 | bibcode=2015PhRvB..91i4507H | doi-access=free }}</ref> In particular, although the non-trivial topology is expected to give rise to protected chiral edge states, due to U(1) symmetry-breaking the edge current is not a protected quantity. In fact, it has been shown that the edge current vanishes identically for any higher angular momentum chiral pairing states which feature even larger Chern numbers, such as chiral d-, f-wave etc.<ref>{{cite journal | last1=Huang | first1=Wen | last2=Taylor | first2=Edward | last3=Kallin | first3=Catherine | title=Vanishing edge currents in non-p-wave topological chiral superconductors | journal=Physical Review B | volume=90 | issue=22 | date=2014-12-19 | issn=1098-0121 | doi=10.1103/physrevb.90.224519 | page=224519| arxiv=1410.0377 | bibcode=2014PhRvB..90v4519H | s2cid=118773764 }}</ref><ref>{{cite journal | last1=Tada | first1=Yasuhiro | last2=Nie | first2=Wenxing | last3=Oshikawa | first3=Masaki | title=Orbital Angular Momentum and Spectral Flow in Two-Dimensional Chiral Superfluids | journal=Physical Review Letters | volume=114 | issue=19 | date=2015-05-13 | issn=0031-9007 | doi=10.1103/physrevlett.114.195301 | page=195301| pmid=26024177 | arxiv=1409.7459 | bibcode=2015PhRvL.114s5301T | s2cid=3152887 }}</ref>

T_c seems to increase under uniaxial compression<ref>{{cite journal|last1=Steppke|first1=Alexander|last2=Zhao|first2=Lishan|last3=Barber|first3=Mark E.|last4=Scaffidi|first4=Thomas|last5=Jerzembeck|first5=Fabian|last6=Rosner|first6=Helge|last7=Gibbs|first7=Alexandra S.|last8=Maeno|first8=Yoshiteru|last9=Simon|first9=Steven H.|last10=Mackenzie|first10=Andrew P.|last11=Hicks|first11=Clifford W.|date=2017-01-12|title=Strong peak in T_c of Sr₂RuO₄ under uniaxial pressure|url=http://pure-oai.bham.ac.uk/ws/files/102786770/Hicks_2017_Science.pdf|journal=Science|publisher=American Association for the Advancement of Science (AAAS)|volume=355|issue=6321|page=eaaf9398|doi=10.1126/science.aaf9398|issn=0036-8075|pmid=28082534|hdl-access=free|hdl=10023/10113|s2cid=8197509}}</ref> that pushes the [[van Hove singularity]] of the d_xy orbital across the Fermi level.<ref>{{Cite journal|last1=Sunko|first1=Veronika|last2=Abarca Morales|first2=Edgar|last3=Marković|first3=Igor|last4=Barber|first4=Mark E.|last5=Milosavljević|first5=Dijana|last6=Mazzola|first6=Federico|last7=Sokolov|first7=Dmitry A.|last8=Kikugawa|first8=Naoki|last9=Cacho|first9=Cephise|last10=Dudin|first10=Pavel|last11=Rosner|first11=Helge|date=2019-08-19|title=Direct observation of a uniaxial stress-driven Lifshitz transition in Sr₂RuO₄|url=https://www.nature.com/articles/s41535-019-0185-9|journal=NPJ Quantum Materials|language=en|volume=4|issue=1|page=46|doi=10.1038/s41535-019-0185-9 | arxiv=1903.09581 |bibcode=2019npjQM...4...46S|s2cid=85459284|issn=2397-4648}}</ref>

In August 2021 evidenceEvidence was reported for ''p''-wave singlet state as in cuprates and conventional superconductors, instead of the conjectured more unconventional ''p''-wave triplet state.<ref>{{Cite journal|last1=Chronister|first1=Aaron|last2=Pustogow|first2=Andrej|last3=Kikugawa|first3=Naoki|last4=Sokolov|first4=Dmitry A.|last5=Jerzembeck|first5=Fabian|last6=Hicks|first6=Clifford W.|last7=Mackenzie|first7=Andrew P.|last8=Bauer|first8=Eric D.|last9=Brown|first9=Stuart E.|date=2021-06-22|title=Evidence for even parity unconventional superconductivity in Sr₂RuO₄|journal=Proceedings of the National Academy of Sciences|language=en|volume=118|issue=25|doi=10.1073/pnas.2025313118 |pmc=8237678|issn=0027-8424|pmid=34161272|arxiv=2007.13730|bibcode=2021PNAS..11825313C}}</ref><ref>{{Cite journal|last=Lopatka|first=Alex|date=2021-08-05|title=An unconventional superconductor isn't so odd after all|journal=Physics Today|volume=2021|pages=0805a|url=https://physicstoday.scitation.org/do/10.1063/PT.6.1.20210805a/abs/|language=en|doi=10.1063/PT.6.1.20210805a|s2cid=241654779}}</ref> It has also been suggested that Strontium ruthenate superconductivity could be due to a [[Fulde–Ferrell–Larkin–Ovchinnikov phase]].<ref>{{Cite journal |last=Kinjo |first=K. |last2=Manago |first2=M. |last3=Kitagawa |first3=S. |last4=Mao |first4=Z. Q. |last5=Yonezawa |first5=S. |last6=Maeno |first6=Y. |last7=Ishida |first7=K. |date=2022-04-22 |title=Superconducting spin smecticity evidencing the Fulde-Ferrell-Larkin-Ovchinnikov state in Sr 2 RuO 4 |url=https://www.science.org/doi/10.1126/science.abb0332 |journal=Science |language=en |volume=376 |issue=6591 |pages=397–400 |doi=10.1126/science.abb0332 |issn=0036-8075}}</ref><ref>{{Cite journal |date=2022-06-13 |title=Magnetic field induces spatially varying superconductivity |url=https://physicstoday.scitation.org/do/10.1063/PT.6.1.20220613a/full |journal=Physics Today |language=en |volume=2022 |issue=1 |pages=0613a |doi=10.1063/PT.6.1.20220613a}}</ref>

Strontium ruthenate behaves as a conventional [[Fermi liquid]] at temperatures below 25 K.<ref>{{cite book|last=Yanoff|first=Brian|title=Temperature dependence of the penetration depth in the unconventional superconductor Sr₂RuO₄|year=2000|publisher=University of Illinois at Urbana-Champaign|url=http://groups.mrl.uiuc.edu/dvh/theses/yanoff.pdf}}</ref>

==References==

{{reflist}}

==ExtraFurther reading==

*{{cite journal |last=Armitage |first=N. Peter |title=Superconductivity mystery turns 25 |journal=Nature |date=9 December 2019 |volume=576 |issue=7787 |pages=386–387 |doi=10.1038/d41586-019-03734-7|pmid=31844256 |doi-access=free }}

*{{cite web|last=Wooten|first=Rachel|title=Strontium Ruthenate|url=https://docs.google.com/viewer?a=v&q=cache:DgnknpjYbx4J:sces.phys.utk.edu/~dagotto/condensed/HW2_2008/Strontium_Ruthenate.ppt+&hl=en&gl=us&pid=bl&srcid=ADGEESjZ7iZGRQSADAb7Z1s_9eAna1xiWVss132uKFgZzdWLT0aMoimFedsvEYqudjD3jQQnZj0ttTougqs1felMdAWruV20EbFHDcoyabxp8gHZE7bmi1WI28B0Y5qLzU42RqJuuJwO&sig=AHIEtbTQVVf6y8oDl63wDTUkXKH9NrNEug&pli=1|publisher=University of Tennessee-Knoxville|access-date=16 April 2012}}<

*{{cite journal|author1=Yoshiteru Maeno|author2=Maurice Rice |author3=Manfred Sigrist |title=The intriguing superconductivity of Strontium Ruthenate|journal=Physics Today|year=2001|volume=54|issue=1|doi=10.1063/1.1349611|url=http://www.physics.mcmaster.ca/~imai/PhysicsToday_2001.pdf|access-date=16 April 2012|bibcode = 2001PhT....54a..42M|pages=42 |doi-access=free}}

*{{cite journal|author1=Yoshiteru Maeno|author2=H. Hashimoto |title=Superconductivity in a layered perovskite without copper|journal=Nature|year=1994|volume=372|pages=532–534|doi=10.1038/372532a0|bibcode = 1994Natur.372..532M|issue=6506 |s2cid=4303356|display-authors=etal}}

{{Strontium compounds}}