Phase relations in superconductor–normal metal–superconductor tunnel junctions

Abstract

The phase difference φ, between the superconducting terminals in superconductor-normal metalsuperconductor tunnel junctions (SINIS), incorporates the phase differences χ1,2 across thin interfaces of constituent SIN junctions and the phase incursion ϕ between the side faces of the central electrode of length L. It is demonstrated here that χ1,2 pass through over their proximity-reduced domain twice, there and back, while φ changes over the single period. Two corresponding solutions, that describe the double-valued order-parameter dependence on χ1,2, jointly form the single-valued dependence on φ, operating in two adjoining regions of φ. The phase incursion ϕ plays a crucial role in creating such a behavior. The current-phase relation j(φ, L) is composed of the two solutions and, at a fixed small L, is characterized by the phase-dependent effective transmission coefficient.

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

“…The boundary conditions (6) have been used for describing single and double Josephson junctions within the GL theory [20,40,[72][73][74][75][76][77].…”

“…When a normal metal is placed between the superconductors, the Josephson coupling emerges as a consequence of superconducting correlations generated by proximity effects in the normal metal region [22][23][24][25][26]. A number of hybrid systems with proximity-induced Josephson coupling through normal metal electrodes, have recently been the focus of scientific scrutiny [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

“…On the other hand, in microscopic theories of the superconducting double junctions a negligible current-induced phase incursion is usually assumed, as distinct from the phase drops [10,13,26,44]. Although the latter point is applied to SISIS junctions in a wide range of realistic parameters, the range gets narrower in SINIS junctions, where both χ 1,2 and ϕ should, generally speaking, be taken into account for describing the transport at mesoscopic values of L [40].…”

“…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.…”

“…It is one of the consequences of the broken correspondence that the 4πperiodic current-phase relation j = j c sin φ 2 , which is based on the simple equalities χ 1,2 = χ, j = j c sin χ, φ = 2χ, does not hold in the double tunnel junctions over the entire range of φ even when the phase incursion and proximity effects are negligibly small. This paper gives an overview of the results relating to the internal phase differences in symmetric SINIS and SISIS double junctions, obtained within the GL approach involving the boundary conditions for the order parameter that take into account the Josephson coupling through interfaces [20,40]. The problem of the corresponding boundary conditions will be discussed in detail below.…”