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| A [[Josephson Junction]] is a quantum mechanical device, which is made of two superconducting electrodes separated by a barrier (insulating tunnel barrier, thin normal metall, etc.).
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| A '''<math>\pi</math> Josephson junction''' is a specific example of a Josephson junction which has a [[Josephson phase]] φ of <math>\pi</math> in the ground state i.e. when no external current or magnetic field is applied.
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| ==Background==
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| The [[supercurrent]] ''I<sub>s</sub>'' through a conventional [[Josephson junction]] (JJ) is given by ''I<sub>s</sub> = I<sub>c</sub>sin(φ)'', | |
| where φ is the phase difference of the superconducting wave functions of the two
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| electrodes, i.e. the [[Josephson phase]].<ref>
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| {{cite journal
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| |author = B. D. Josephson
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| |year = 1962
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| |title = Possible New Effects in Superconducting Tunnelling
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| |journal = Physics Letters
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| |volume = 1
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| |pages = 251
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| |doi = 10.1016/0031-9163(62)91369-0
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| |bibcode = 1962PhL.....1..251J
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| |issue = 7 }}</ref> The critical current ''I<sub>c</sub>'' is the maximum supercurrent that can flow through the Josephson junction. In experiment, one usually applies some current through the Josephson junction and the junction reacts by changing the Josephson phase. From the above formula it is clear that the phase ''φ = arcsin(I/I<sub>c</sub>)'', where ''I'' is the applied (super)current.
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| Since the phase is <math>2\pi</math>-periodic, i.e. <math>\phi</math> and <math>\phi+2\pi n</math> are physically equivalent, without losing generality, we restrict the discussion below to the interval <math> 0 \leq \phi < 2\pi</math>.
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| When no current (''I'' = 0) is passing through the Josephson junction, e.g. when the junction is disconnected, the junction is in the ground state and the Josephson phase across it is zero (φ = 0). The phase can also be <math>\phi=\pi</math>, also resulting in no current through the junction. It turns out that the state with <math>\phi=\pi</math> is ''unstable'' and corresponds to the [[Josephson energy]] maximum, while the state φ = 0 corresponds to the [[Josephson energy]] minimum and ''is'' a ground state.
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| In certain cases one may obtain a Josephson junction where the critical current is negative (''I<sub>c</sub> < 0''). In this case, the first Josephson relation becomes
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| :<math> I_s = -|I_c|\sin(\phi) = |I_c|\sin(\phi+\pi)</math>
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| Obviously, the ground state of such a Josephson junction is <math>\phi=\pi</math> and corresponds to the [[Josephson energy]] minimum, while the conventional state φ = 0 is unstable and corresponds to the [[Josephson energy]] maximum. Such a Josephson junction with <math>\phi=\pi</math> in the ground state is called a '''<math>\pi</math> Josephson junction'''.
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| <math>\pi</math> Josephson junctions have quite unusual properties. For example, if one connects (shorts) the superconducting electrodes with the inductance ''L'' (e.g. superconducting wire), one may expect the spontaneous supercurrent circulating in the loop, passing through the junction and through inductance clockwise or counterclockwise. This supercurrent is spontaneous and belongs to the ground state of the system. The direction of its circulation is chosen at random. This supercurrent will of course induce a magnetic field which can be detected experimentally. The magnetic flux passing through the loop will have the value from 0 to a half of [[magnetic flux quanta]], i.e. from 0 to Φ<sub>0</sub>/2, depending on the value of inductance ''L''.
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| ==Technologies and physical principles==
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| *'''Ferromagnetic Josephson junctions'''. Consider a [[Josephson junction]] with a ferromagnetic Josephson barrier, i.e. the multilayers '''S'''uperconductor-'''F'''erromagnet-'''S'''uperconductor (SFS) or '''S'''uperconductor-'''I'''nsulator-'''F'''erromagnet-'''S'''uperconductor (SIFS). In such structures the superconducting order parameter inside the F-layer oscillates in the direction perpendicular to the junction plane. As a result, for certain thicknesses of the F-layer and temperatures, the order parameter may become +1 at one superconducting electrode and -1 at the other superconducting electrode. In this situation one gets a <math>\pi</math> Josephson junction. Note that inside the F-layer the competition of different solutions takes place and the one with the lower energy wins out. Various ferromagnetic <math>\pi</math> junctions have been fabricated: SFS junctions with weak ferromagnetic interlayers;<ref name="Ryazanov:SFS">
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| {{cite journal
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| |author = V.V.Ryazanov, V.A.Oboznov, A.Yu.Rusanov, A.V.Veretennikov, A.A.Golubov and J.Aarts
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| |year = 2001
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| |title = Coupling of two superconductors through a ferromagnet: evidence of a <math>\pi</math>-junction
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| |journal = Physical Review Letters
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| |volume = 86
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| |pages = 2427–30
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| |doi = 10.1103/PhysRevLett.86.2427
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| |pmid = 11289946
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| |issue = 11
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| |bibcode=2001PhRvL..86.2427R
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| |arxiv = cond-mat/0008364 }}</ref> SFS junctions with strong ferromagnetic interlayers, such as Co, Ni,<ref name="Bannykh:SIFS">
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| {{cite journal
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| |author = A. A. Bannykh, J. Pfeiffer, V. S. Stolyarov, I. E. Batov, V. V. Ryazanov, and M. Weides
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| |year = 2009
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| |title = Josephson tunnel junctions with a strong ferromagnetic interlayer
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| |journal = Physical Review B
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| |volume = 79
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| |pages = 054501
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| |doi = 10.1103/PhysRevB.79.054501
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| |issue = 5
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| |bibcode = 2009PhRvB..79e4501B |arxiv = 0808.3332 }}</ref> and NiFe<ref name="Robinson:SFS">
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| {{cite journal
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| |author = J.W.A. Robinson, S. Piano, G. Burnell, C. Bell and M. G. Blamire
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| |year = 2006
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| |title = Critical Current Oscillations in Strong Ferromagnetic <math>\pi</math> Junctions
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| |journal = Physical Review Letters
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| |volume = 97
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| |pages = 177003
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| |doi = 10.1103/PhysRevLett.97.177003
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| |pmid = 17155498
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| |issue = 17
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| |bibcode=2006PhRvL..97q7003R
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| |arxiv = cond-mat/0606067 }}</ref> SIFS junctions;<ref name="Kontos:SIFS">
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| {{cite journal
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| |author = T. Kontos, M. Aprili, J. Lesueur and X. Grison
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| |year = 2002
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| |title = Josephson Junction through a Thin Ferromagnetic Layer: Negative Coupling
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| |journal = Physical Review Letters
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| |volume = 89
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| |pages = 137007
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| |doi = 10.1103/PhysRevLett.89.137007
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| |pmid = 12225057
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| |issue = 13
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| |bibcode=2002PhRvL..89m7007K
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| }}</ref><ref name="Weides:SIFS">
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| {{cite journal
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| |author = M. Weides, M. Kemmler, H. Kohlstedt, A. Buzdin, E. Goldobin, D. Koelle, and R. Kleiner
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| |year = 2006
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| |title = High quality ferromagnetic 0 and pi Josephson tunnel junctions
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| |journal = Applied Physics Letters
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| |volume = 89
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| |pages = 122511
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| |doi = 10.1063/1.2356104
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| |issue = 12
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| |arxiv = cond-mat/0604097 |bibcode = 2006ApPhL..89l2511W }}</ref> and S-Fi-S junctions.<ref name="Vavra:SFiS">
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| {{cite journal
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| |author = O. Vavra, S. Gazi, D. S. Golubovic, I. Vavra, J. Derer, J. Verbeeck, G. Van Tendeloo, V. V. Moshchalkov
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| |year = 2006
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| |title = 0 and <math>\pi</math> phase Josephson coupling through an insulating barrier with magnetic impurities
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| |journal = Physical Review B
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| |volume = 74
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| |pages = 020502,
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| |doi = 10.1103/PhysRevB.74.020502|arxiv = cond-mat/0606513 |bibcode = 2006PhRvB..74b0502V
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| |issue = 2 }}
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| </ref>
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| *'''Josephson junctions with unconventional order parameter symmetry'''. Novel superconductors, notably high temperature cuprate superconductors, have an anisotropic [[Ginzburg-Landau Theory|superconducting order parameter]] which can change its sign depending on the direction. In particular, a so-called d-wave order parameter has a value of +1 if one looks along the crystal axis ''a'' and –1 if one looks along the crystal axis ''b''. If one looks along the ''ab'' direction (45° between ''a'' and ''b'') the order parameter vanishes. By making Josephson junctions between d-wave superconducting films with different orientations or between d-wave and conventional isotropic s-wave superconductors, one can get a phase shift of <math>\pi</math>. Nowadays there are several realizations of <math>\pi</math> Josephson junctions of this type:
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| **tri-crystal grain boundary Josephson junctions,<ref>{{cite journal|doi=10.1103/RevModPhys.72.969|journal=Reviews of Modern Physics|volume=72|pages=969–1016|year=2000|title=Pairing symmetry in cuprate superconductors|last1=Tsuei|first1=C. C.|last2=Kirtley|first2=J. R.|bibcode=2000RvMP...72..969T|issue=4}}</ref>
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| **tetra-crystal grain boundary Josephson junctions,<ref>{{cite journal|doi=10.1002/(SICI)1521-3889(199909)8:6<511::AID-ANDP511>3.0.CO;2-K
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| |title=Magnetic field dependencies of the critical current and of the resonant modes of dc SQUIDs fabricated from superconductors with s + idx^2-y^2 order-parameter symmetries|
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| author=B. Chesca|journal=Annalen der Physik|volume=8|year=1999|page=511|bibcode = 1999AnP...511..511C }}</ref><ref>{{cite journal|doi=10.1063/1.125627|title=Design and realization of an all d-wave dc π-superconducting quantum interference device|year=2000|last1=Schulz|first1=R. R.|first2=B.|first3=B|first4=C.W.|first5=A.|first6=H.|first7=H.|first8=J.|first9=C.C.|journal=Applied Physics Letters|volume=76|pages=912|last2=Chesca|last3=Goetz|last4=Schneider|last5=Bielefeldt|last6=Hilgenkamp|last7=Mannhart|last8=Tsuei|bibcode = 2000ApPhL..76..912S }}</ref>
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| **d-wave/s-wave ramp zigzag JJs Josephson junctions,<ref name=r1>{{cite journal|doi=10.1103/RevModPhys.67.515|title=Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors—Evidence for dx^2-y^2 symmetry|year=1995|last1=Van Harlingen|first1=D. J.|journal=Reviews of Modern Physics|volume=67|pages=515|bibcode=1995RvMP...67..515V|issue=2}}</ref><ref>{{cite journal|doi=10.1103/PhysRevLett.88.057004|title=d-Wave–Induced Josephson Current Counterflow in YBa_{2}Cu_{3}O_{7}/Nb Zigzag Junctions|year=2002|last1=Smilde|first1=H. J. H.|first3=D. H. A.|first4=G. J.|first5=H.|first6=H.|journal=Physical Review Letters|volume=88|pages=057004|bibcode=2002PhRvL..88e7004S}}</ref><ref>{{cite journal|doi=10.1038/nature01442|title=Ordering and manipulation of the magnetic moments in large-scale superconducting π-loop arrays|year=2003|last1=Hilgenkamp|first1=Hans|first3=Henk-Jan H.|first4=Dave H. A.|first5=Guus|first6=Horst|first7=John R.|first8=Chang C.|journal=Nature|volume=422|pages=50–3|pmid=12621428|last3=Smilde|last4=Blank|last5=Rijnders|last6=Rogalla|last7=Kirtley|last8=Tsuei|issue=6927|last2=Ariando|bibcode = 2003Natur.422...50H }}</ref><ref>{{cite journal|doi=10.1103/PhysRevLett.94.167001|title=Phase-Sensitive Order Parameter Symmetry Test Experiments Utilizing Nd_{2-x}Ce_{x}CuO_{4-y}/Nb Zigzag Junctions|year=2005|last1=Ariando|first2=D.|first3=H. -J. H.|first4=V.|first5=D. H. A.|first6=H.|first7=H.|journal=Physical Review Letters|volume=94|pages=167001|bibcode=2005PhRvL..94p7001A|arxiv = cond-mat/0503429 }}</ref>
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| **tilt-twist grain boundary Josephson junctions,<ref>{{cite journal|doi=10.1103/PhysRevLett.89.207001|title=Intrinsic d-Wave Effects in YBa_{2}Cu_{3}O_{7-δ} Grain Boundary Josephson Junctions|year=2002|last1=Lombardi|first1=F.|first2=F.|first3=F.|first4=F. Miletto|first5=A.|first6=G.|first7=E|first8=J. R.|first9=C. C.|journal=Physical Review Letters|volume=89|pages=207001|bibcode=2002PhRvL..89t7001L}}</ref>
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| **p-wave based Josephson junctions.
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| *'''S'''uperconductor-'''N'''ormalMetal-'''S'''uperconductor (SNS) Josephson junctions with nonequlibrium electron distribution in N-layer.<ref name="Beselmans:NonEqPiJJ">
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| {{cite journal
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| |author = J. J. A. Baselmans, A. F. Morpurgo, B. J. Van Wees, T. M. Klapwijk
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| |title=Reversing the direction of the supercurrent in a controllable Josephson junction
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| |journal=Nature
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| |year=1999
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| |volume=397
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| |pages=43–45
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| |doi = 10.1038/16204|bibcode = 1999Natur.397...43B
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| |issue=6714}}</ref>
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| *Superconductor-'''[[Quantum Dot]]'''-Superconductor (S-QuDot-S) Josephson junctions (implemented by [[carbon nanotube]] Josephson junctions).<ref name="CNT-JJ">
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| {{cite journal
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| |author = J-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu, M. Monthioux
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| |title=Carbon nanotube Superconducting Quantum Interference Device
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| |journal=Nature Nanotechnology
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| |year=2006
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| |volume=1
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| |pages=53–9|doi = 10.1038/nnano.2006.54
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| |pmid = 18654142
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| |issue = 1|bibcode = 2006NatNa...1...53C }}
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| </ref>
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| ==Historical developments==
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| Theoretically, the first time the possibility of creating a <math>\pi</math> Josephson junction was discussed by Bulaevskii ''et al.''
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| ,<ref name="Bulaevskii:pi-loop">
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| {{cite journal
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| |author = L. N. Bulaevskii, V. V. Kuzii, A. A. Sobyanin
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| |title = Superconducting system with weak coupling to the current in the ground state
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| |journal = JETP Letters
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| |volume = 25
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| |pages = 290–294,
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| |year = 1977|bibcode = 1977JETPL..25..290B
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| |last2 = Kuziǐ
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| |last3 = Sobyanin }}
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| </ref> who considered a Josephson junction with paramagnetic scattering in the barrier. Almost one decade later, the possibility of having a <math>\pi</math> Josephson junction was discussed in the context of heavy fermion p-wave superconductors.<ref name="Geshkenbein">
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| {{cite journal
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| |author = V. B. Geshkenbein, A. I. Larkin, A. Barone
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| |title = Vortices with half magnetic flux quanta in heavy-fermion superconductors
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| |journal = Physical Review B
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| |year = 1987
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| |volume=36
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| |pages= 235–238
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| |doi = 10.1103/PhysRevB.36.235|bibcode = 1987PhRvB..36..235G }}
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| </ref>
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| Experimentally, the first <math>\pi</math> Josephson junction was a corner junction made of [[yttrium barium copper oxide]] (d-wave) and [[lead|Pb]] (s-wave) superconductors.<ref name=r1/> The first unambiguous proof of a <math>\pi</math> Josephson junction with a ferromagnetic barrier was given only a decade later.<ref name="Ryazanov:SFS"/> That work used a weak ferromagnet consisting of an copper-nickel alloy (Cu<sub>x</sub>Ni<sub>1-x</sub>, with ''x'' around 0.5) and optimized it so that the [[Curie temperature]] was close to the superconducting transition temperature of the superconducting [[niobium]] leads.
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| ==See also==
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| *[[Josephson junction]]
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| *[[Varphi Josephson junction|φ Josephson junction]]
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| *[[Semifluxon]]
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| *[[Fractional vortices]]
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| *[[Brian D. Josephson]]
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| ==References==
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| {{reflist|2}}
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| [[Category:Superconductivity]]
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| [[Category:Josephson effect]]
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