Pi Josephson junction
Encyclopedia
A Josephson Junction is a voltage-to-frequency converter usefully sensitive to voltage, current and magnetic fields that is made of a superconducting wire interrupted by an insulating weak-link.
A
Josephson junction is a specific example of a Josephson junction which has a Josephson phase
φ of
in the ground state when no external current or magnetic field is applied.
Is through a conventional Josephson junction (JJ) is given by Is = Icsin(φ),
where φ is the phase difference of the superconducting wave functions of the two
electrodes, i.e. the Josephson phase
. The critical current Ic 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/Ic), where I is the applied (super)current.
Since the phase is
-periodic, i.e. 
and 
are physically equivalent, without losing generality, we restrict the discussion below to the interval 0 < φ < 2
.
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
, also resulting in no current through the junction. It turns out that the state with 
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.
In certain cases one may obtain a Josephson junction where the critical current is negative (Ic < 0). In this case, the first Josephson relation becomes
Obviously, the ground state of such a Josephson junction is
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
in the ground state is called a 
Josephson junction.
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 Φ0/2, depending on the value of inductance L.
Josephson junction was discussed by Bulaevskii et al.
, who considered a Josephson junction with paramagnetic scattering in the barrier. Almost one decade later, the possibility of having a
Josephson junction was discussed in the context of heavy fermion p-wave superconductors.
Experimentally, the first
Josephson junction was a corner junction made of yttrium barium copper oxide
(d-wave) and Pb
(s-wave) superconductors. The first unambiguous proof of a
Josephson junction with a ferromagnetic barrier was given only a decade later. That work used a weak ferromagnet consisting of an copper-nickel alloy (CuxNi1-x, 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.
A
Josephson junction is a specific example of a Josephson junction which has a Josephson phaseJosephson phase
In superconductivity, the Josephson phase is the difference of the phases of the quantum mechanical wave function in two superconducting electrodes forming a Josephson junction....
φ of
in the ground state when no external current or magnetic field is applied.Background
The supercurrentSupercurrent
A supercurrent is a superconducting current, that is, electric current which flows without dissipation....
Is through a conventional Josephson junction (JJ) is given by Is = Icsin(φ),
where φ is the phase difference of the superconducting wave functions of the two
electrodes, i.e. the Josephson phase
Josephson phase
In superconductivity, the Josephson phase is the difference of the phases of the quantum mechanical wave function in two superconducting electrodes forming a Josephson junction....
. The critical current Ic 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/Ic), where I is the applied (super)current.
Since the phase is
-periodic, i.e. and are physically equivalent, without losing generality, we restrict the discussion below to the interval 0 < φ < 2.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
, also resulting in no current through the junction. It turns out that the state with is unstable and corresponds to the Josephson energyJosephson energy
In superconductivity, the Josephson energy is the potential energy accumulated in the Josephson junction when a supercurrent flows through it. One can think about a Josephson junction as about a non-linear inductance which accumulates energy when a current passes through it...
maximum, while the state φ = 0 corresponds to the Josephson energy
Josephson energy
In superconductivity, the Josephson energy is the potential energy accumulated in the Josephson junction when a supercurrent flows through it. One can think about a Josephson junction as about a non-linear inductance which accumulates energy when a current passes through it...
minimum and is a ground state.
In certain cases one may obtain a Josephson junction where the critical current is negative (Ic < 0). In this case, the first Josephson relation becomes
Obviously, the ground state of such a Josephson junction is
and corresponds to the Josephson energyJosephson energy
In superconductivity, the Josephson energy is the potential energy accumulated in the Josephson junction when a supercurrent flows through it. One can think about a Josephson junction as about a non-linear inductance which accumulates energy when a current passes through it...
minimum, while the conventional state φ = 0 is unstable and corresponds to the Josephson energy
Josephson energy
In superconductivity, the Josephson energy is the potential energy accumulated in the Josephson junction when a supercurrent flows through it. One can think about a Josephson junction as about a non-linear inductance which accumulates energy when a current passes through it...
maximum. Such a Josephson junction with
in the ground state is called a Josephson junction. 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 Φ0/2, depending on the value of inductance L.Technologies and physical principles
- Ferromagnetic Josephson junctions. Consider a Josephson junction with a 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 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
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 
junctions have been fabricated: SFS junctions with weak ferromagnetic interlayers; SFS junctions with strong ferromagnetic interlayers, such as Co, Ni, and NiFe SIFS junctions; and S-Fi-S junctions.
- Josephson junctions with unconventional order parameter symmetry. Novel superconductors, notably high temperature cuprate superconductors, have an anisotropic superconducting order parameterGinzburg-Landau theoryIn physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity...
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
. Nowadays there are several realizations of 
Josephson junctions of this type:
- tri-crystal grain boundary Josephson junctions,
- tetra-crystal grain boundary Josephson junctions,
- d-wave/s-wave ramp zigzag JJs Josephson junctions,
- tilt-twist grain boundary Josephson junctions,
- p-wave based Josephson junctions.
- Superconductor-NormalMetal-Superconductor (SNS) Josephson junctions with nonequlibrium electron distribution in N-layer.
- Superconductor-Quantum DotQuantum dotA quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...
-Superconductor (S-QuDot-S) Josephson junctions (implemented by carbon nanotubeCarbon nanotubeCarbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...
Josephson junctions).
Historical developments
Theoretically, the first time the possibility of creating a Josephson junction was discussed by Bulaevskii et al., who considered a Josephson junction with paramagnetic scattering in the barrier. Almost one decade later, the possibility of having a
Josephson junction was discussed in the context of heavy fermion p-wave superconductors.Experimentally, the first
Josephson junction was a corner junction made of yttrium barium copper oxideYttrium barium copper oxide
Yttrium barium copper oxide, often abbreviated YBCO, is a crystalline chemical compound with the formula YBa2Cu3O7. This material, a famous "high-temperature superconductor", achieved prominence because it was the first material to achieve superconductivity above the boiling point of liquid...
(d-wave) and Pb
Lead
Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...
(s-wave) superconductors. The first unambiguous proof of a
Josephson junction with a ferromagnetic barrier was given only a decade later. That work used a weak ferromagnet consisting of an copper-nickel alloy (CuxNi1-x, with x around 0.5) and optimized it so that the Curie temperature was close to the superconducting transition temperature of the superconducting niobiumNiobium
Niobium or columbium , is a chemical element with the symbol Nb and atomic number 41. It's a soft, grey, ductile transition metal, which is often found in the pyrochlore mineral, the main commercial source for niobium, and columbite...
leads.
See also
- Josephson junction
- SemifluxonSemifluxonIn superconductivity, a Semifluxon is a vortex of supercurrent carrying the magnetic flux equal to the half of the magnetic flux quantum. Semifluxons exist in the so-called 0-π long Josephson junctions at the boundary between 0 and π regions. For a shorter junction length In superconductivity, a...
- Fractional vortices
- Brian D. Josephson