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 π Josephson junction is a Josephson junction in which the Josephson phase φ equals π in the ground state, i.e. when no external current or magnetic field is applied. 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 π Josephson junction is a Josephson junction in which the Josephson phase φ equals π in the ground state, i.e. when no external current or magnetic field is applied. The supercurrent Is through a Josephson junction (JJ) is generally given by Is = Icsin(φ),where φ is the phase difference of the superconducting wave functions of the twoelectrodes, 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 2π-periodic, i.e. φ and φ + 2πn are physically equivalent, without losing generality, we restrict the discussion below to the interval 0 ≤ φ < 2π. 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 φ = π, also resulting in no current through the junction. It turns out that the state with φ = π 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 ϕ = π {displaystyle phi =pi } 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 ϕ = π {displaystyle phi =pi } in the ground state is called a π Josephson junction. π 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. Theoretically, the first time the possibility of creating a π {displaystyle pi } 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 π {displaystyle pi } Josephson junction was discussed in the context of heavy fermion p-wave superconductors. Experimentally, the first π {displaystyle pi } 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 π {displaystyle pi } Josephson junction with a ferromagnetic barrier was given only a decade later. That work used a weak ferromagnet consisting of a 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.