Pi Josephson junction

A Josephson junction is a quantum mechanical device which is made of two superconducting electrodes separated by a barrier (thin insulating tunnel barrier, normal metal, semiconductor, ferromagnet, etc.). 
A Josephson junction is a Josephson junction in which the Josephson phase "φ" equals in the ground state, i.e. when no external current or magnetic field is applied.
Background.
The supercurrent "I""s" through a Josephson junction (JJ) is generally given by "I""s" = "I""c"sin("φ"),
where φ is the phase difference of the superconducting wave functions of the two
electrodes, i.e. the Josephson phase. 
The critical current "I""c" is the maximum supercurrent that can exist through the Josephson junction. 
In experiment, one usually causes 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""c"), where "I" is the applied (super)current.
Since the phase is 2-periodic, i.e. "φ" and "φ" + 2"n" are physically equivalent, without losing generality, the discussion below refers to the interval 0 ≤ "φ" < 2.
When no current ("I" = 0) exists 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 "φ" = , also resulting in no current through the junction. It turns out that the state with "φ" =  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 ("I""c" < 0). In this case, the first Josephson relation becomes
The ground state of such a Josephson junction is formula_2 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 formula_2 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".
Historical developments.
Theoretically, the first time the possibility of creating a formula_4 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 formula_4 Josephson junction was discussed in the context of heavy fermion p-wave superconductors.
 Experimentally, the first formula_4 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 formula_4 Josephson junction with a ferromagnetic barrier was given only a decade later. That work used a weak ferromagnet consisting of a copper-nickel alloy (Cu"x"Ni1−"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.