The current-phase relation in Josephson junctions

Abstract

This review provides a theoretical basis for understanding the current-phase relation (C⌽R) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the C⌽R from the standard sinusoidal form. A new experimental tool for measuring the C⌽R is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the C⌽R measurements for both fundamental physics and applications.

Current-Phase Relationship, Thermal and Quantum Phase Slips in Superconducting Nanowires Made on a Scaffold Created Using Adhesive Tape

“…Inset: An example plot of the LY multivalued CPR [11,12] (Figure 3c and 3d). In the calculation, the current widths corresponding to each voltage plateau in the three cases considered above oscillate with power but do not go to zero at any power.…”

Josephson current through superconductor/diffusive-normal-metal/superconductor junctions: Interference effects governed by pairing symmetry

“…͑6͒ for all wave numbers. Actually, the low-temperature anomaly of the Josephson current has been reported [15][16][17][18]24,25 in SIS junctions of these symmetries. The absence of the proximity effect in diffusive normal metals is described by a relation [26][27][28] …”

“…13 The MARS spatially localizes at a distance of 0 = ប v F / ⌬ 0 from the surface 14 and energetically forms just on the Fermi energy, where 0 is the coherence length, v F = ប k F / m is the Fermi velocity, k F is the Fermi wave number, and m is the mass of an electron. The low-temperature anomaly of the Josephson current in SIS junctions of unconventional superconductors [15][16][17][18][19][20][21][22][23][24][25] is a consequence of the resonant tunneling of Cooper pairs through the MARS.…”

Upper bound on the Andreev states induced second harmonic in the Josephson coupling ofYBa2Cu3O7−δ/NbChesca1, Smilde2, Hilgenkamp3 2008Phys. Rev. B310130View full textAdd to dashboardCite

“…A key element, namely, the knowledge of the current-phase relation ͑CPR͒ of the Josephson current, remains unsettled. 6 It has been predicted [7][8][9][10][11] that zero-energy Andreev states ͑ZES͒ formed at the d-wave junctions interface are expected to induce a second harmonic Josephson current J 2 in the CPR. For various qubit concepts this J 2 is essential, as a superconducting qubit based on J 2 will have an operating point intrinsically stable and protected against the environmental noise, which will reduce decoherence.…”

“…Therefore, its presence cannot be attributed to ZES formation, while there are other alternative mechanisms that may generate it. 6 Thus, in Refs. 27 and 28, a second harmonic has been observed in structures containing YBCO 45°grain-boundary junctions ͑GBJs͒.…”