Proximity-reduced range of internal phase differences in double Josephson junctions with closely spaced interfaces

Abstract

A substantial influence of the proximity and pair breaking effects on the range of internal phase differences is shown to take place in symmetric double Josephson junctions with closely spaced interfaces and to affect the evolution of the supercurrent j with the changing central lead's length L. If the phase difference φ between the external leads is controlled and L exceeds a few coherence lengths, the regime of interchanging modes is established. The range of the phase differences across the two individual interfaces is reduced with decreasing L, and the states of the higher energy mode are gradually eliminated. With a further decrease of L the regime of interchanging modes is destroyed along with the asymmetric mode. The conventional single junction current-phase relation j(φ) is eventually established and the condensate states' doubling is fully removed at very small L.

Phase relations in superconductor–normal metal–superconductor tunnel junctions

“…The phase relations in the SINIS systems do not result in the regime of interchanging modes with abrupt supercurrent changes, that can occur in SISIS junctions. [37][38][39] The small values of the order parameter and supercurrent, that are characteristic for the second solution and marked with crosses in Figs. 3 and 4, are specifically associated with the choice g ℓ = 0.01 for the Josephson coupling constant, taken for demonstrating a quantitative agreement between the numerical and approximate analytical results.…”

“…For superconducting leads real roots usually take nonnegative values t i ≥ 0 (i = 1, 2, 3). 2,3 For the proximity influenced normal metal lead only one of the real roots is nonnegative: t 1 ≥ 0, t 2,3 ≤ 0, as ensured by the sign minus and sign plus on the right hand sides of the first and second equations in (S9), respectively. The sign minus originates from the condition a n > 0 for the normal metal.…”

“…When two superconductors are separated by a thin interface, their phase dependent Josephson coupling generates the Josephson supercurrent through the junction. [1][2][3] If a normal metal is placed between the superconductors with a nonzero interface transparencies (SINIS), their Josephson coupling appears as a corollary of the proximity-induced superconducting correlations in the normal-metal region. [4][5][6][7][8] Various hybrid systems, in which the Josephson coupling through normal metal electrodes is induced by the proximity effect, have recently been the focus of research activities.…”

Boundary conditions for the order parameter and the proximity influenced internal phase differences in double superconducting junctions

“…However, under the opposite condition L ξ, the proximity and interface pair breaking can have a strong effect on the transport processes, including the Josephson current. Static and dynamic interactions of two closely spaced Josephson junctions can manifest in a variety of properties of mesoscopic superconducting heterostructures and play an important role in superconducting electronics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…The latter approach substantially simplifies the solution and, in a variety of cases, can be justified. However, an implicit assumption of such a standard approximation is the one-to-one correspondence between the external φ and internal χ 1,2 phase differences, which recently has been demonstrated to be invalid under certain conditions in the double and multiple junctions [19,20,40]. The one-to-one correspondence gets broken in the SINIS and SISIS superconducting double junctions under two qualitatively different scenarios characteristic of the behavior of internal phase differences driven by the external phase difference and influenced by the proximity and pair breaking effects.…”