Pi Josephson junction

Pi Josephson junction

A pi Josephson Junction is a specific instance of a Josephson Junction where the Josephson phase phi is equal to pi in the ground state, i.e. when no external currents or magnetic fields are applied to the Josephson junction.

Background

The supercurrent I_s through a conventional Josephson junction (JJ) is given by I_s = I_c sin(phi),where phi is the phase difference of the superconducting wave functions of the twoelectrodes, i.e. the Josephson phase [cite journal
author = B. D. Josephson
year = 1962
title = Possible New Effects in Superconducting Tunnelling
journal = Phys. Lett.
volume = 1
pages = 251
doi = 10.1016/0031-9163(62)91369-0
] . The critical current I_c is the maximum supercurrent that can flow through the JJ.In experiment one usually applies some current through the JJ and the junction reacts by changing the Josephson phase. From the above formula it is clear that the phase phi=arcsin(I/I_c), where I is the applied (super)current.

Since the phase is 2pi-periodic, i.e. phi and phi+2pi n are physically equivalent, without losing generality, we restrict the discussion below to the interval 0leqphi<2pi.

When no current (I=0) is passing through the JJ, e.g. when the junction is disconnected, the JJ is in the ground state and the Josephson phase across it is zero (phi=0). Attentive reader may notice, that according to the above equations the phase can also be phi=pi, also resulting in no current through the JJ.It turns out that the state with phi=pi is "unstable" and corresponds to the Josephson energy maximum, while the state phi=0 corresponds to the Josephson energy minimum and "is" a ground state.

In certain cases one may obtain a JJ where the critical current is negative (I_c<0). In this case the first Josephson relation becomes

I_s = -|I_c|sin(phi) = |I_c|sin(phi+pi)

Obviously, the ground state of such a JJ is phi=pi and corresponds to the Josephson energy minimum, while the conventional state phi=0 is unstable and corresponds to the Josephson energy maximum. Such a JJ with phi=pi in the ground state is called pi Josephson junction.

pi Josephson junctions have quite unusual properties. For example, if one connects (shorts) the superconducting electrodes with the inductance L (e.g. superconducting wire), as shown in Fig.???, one may expect the spontaneous supercurrent circulating in the loop, passing through JJ 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 Phi_0/2, depending on the value of inductance L.

Technologies and physical principles

* Ferromagnetic Josephson junctions. Consider a Josephson junction with ferromagnetic Josephson barrier, i.e. the multilayers Superconductor-Ferromagnet-Superconductor (SFS) or Superconductor-Insulator-Ferromagnet-Superconductor (SIFS). In such structures the superconducting order parameter inside F-layer oscillates in the direction perpendicular to the JJ plane. As a result, for certain thicknesses of the F-layer and temperatures, the order parameter may become +1 at one at one superconducting electrode and -1 at the other superconducting electrode. In this situation one gets pi Josephson junction. Note that inside F-layer the competition of different solutions takes place and the one with the lower energy, wins. Ferromagnetic pi junction were fabricated by several groups:
** SFS JJs

cite journal
author = V.V.Ryazanov, V.A.Oboznov, A.Yu.Rusanov, A.V.Veretennikov, A.A.Golubov and J.Aarts
year = 2001
title = Coupling of two superconductors through a ferromagnet: evidence of a pi-junction
journal = Phys. Rev. Lett
volume = 86
pages = 2427
doi = 10.1103/PhysRevLett.86.2427
]
** SFS JJs cite journal
author = J.W.A. Robinson, S. Piano, G. Burnell, C. Bell and M. G. Blamire
year = 2006
title = Critical Current Oscillations in Strong Ferromagnetic pi Junctions
journal = Phys. Rev. Lett
volume = 97
pages = 177003
doi = 10.1103/PhysRevLett.97.177003
]

** SIFS JJs cite journal
author = T. Kontos, M. Aprili, J. Lesueur and X. Grison
year = 2002
title = Josephson Junction through a Thin Ferromagnetic Layer: Negative Coupling
journal = Phys. Rev. Lett.
volume = 89
pages = 137007,
doi = 10.1103/PhysRevLett.89.137007
]

** S-Fi-S JJs cite journal
author = O. Vavra, S. Gazi, D. S. Golubovic, I. Vavra, J. Derer, J. Verbeeck, G. Van Tendeloo, V. V. Moshchalkov
year = 2006
title = 0 and pi phase Josephson coupling through an insulating barrier with magnetic impurities
journal = Phys. Rev. B
volume = 74
pages = 020502,
doi = 10.1103/PhysRevB.74.020502
]

* Josephson junctions with unconventional order parameter symmetry. Novel superconductors, notably high temperature cuprate superconductors, have anisotropic superconducting order parameter which can change its sign depending on the direction. In particular, 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 ab direction (45 degree between a and b) the order parameter vanishes. By making Josephson junctions between d-wave superconducting films with different orientation or between d-wave and conventional isotropic s-wave superconductor, one can get a phase shift of pi. Nowadays there are several realizations of pi JJs of this type:
** tri-crystal grain boundary JJs [http://dx.doi.org/10.1103/10.1103/RevModPhys.72.969 TsueiKirtley Review]
** tetra-crystal grain boundary JJs [Chesca]
** d-wave/s-wave ramp zigzag JJs [http://dx.doi.org/10.1103/RevModPhys.67.515 VanHarlingen Review] , [http://dx.doi.org/10.1103/PhysRevLett.88.057004 SmildeZigZag] , [http://dx.doi.org/10.1038/nature01442 HilgenkampSemifluxons] , [http://dx.doi.org/10.1103/PhysRevLett.94.167001 AriandoZigZag]
** tilt-twist grain boundary JJs [http://dx.doi.org/10.1103/PhysRevLett.89.207001 LombardiTiltTwist]
** p-wave based JJs [???]

* Superconductor-NormalMetal-Superconductor (SNS) Josephson junctions with nonequlibrium electron distribution in N-layer cite journal
author = J. J. A. Baselmans, A. F. Morpurgo, B. J. Van Wees, T. M. Klapwijk
title=Reversing the direction of the supercurrent in a controllable Josephson junction
journal=Nature
year=1999
volume=397
pages=43--45
doi = 10.1038/16204
]

* Superconductor-QuantumDot-Superconductor (S-QuDot-S) JJs (implemented by carbon nanotube based Josephson junctions) cite journal
author = J-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu, M. Monthioux
title=Carbon nanotube Superconducting Quantum Interference Device
journal=Nature Nanotechnology
year=2006
volume=1
pages=53
doi = 10.1038/nnano.2006.54
]

Historical developments

Theoretically, for the first time the possibility to have pi JJs was discussed by Bulaevskii et al. cite journal
author = L. N. Bulaevskii, V. V. Kuzii, A. A. Sobyanin
title = Superconducting system with weak coupling to the current in the ground state
journal = JETP Lett.
volume = 25
pages = 290--294,
year = 1977
] , who considered a JJ with paramagnetic scattering in the barrier. Almost one decade later the possibility of having a pi JJs was discussed in the context of heavy fermion p-wave superconductorcite journal
author = V. B. Geshkenbein, A. I. Larkin, A. Barone
title = Vortices with half magnetic flux quanta in heavy-fermion superconductors
journal = Phys. Rev. B
year = 1987
volume=36
pages= 235--238
doi = 10.1103/PhysRevB.36.235
] .

Experimentally, the first pi JJ was a corner JJ made of YBCO (d-wave) and Pb (s-wave) superconductors, see [http://dx.doi.org/10.1103/RevModPhys.67.515 VanHarlingen Review] . The pi JJs based on ferromagnetic barrier were first fabricated and investigated only a decade later.

ee also

*Josephson junction
*Semifluxon
*Fractional vortices

References


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