Physics of the long range proximity effect

Abstract
The theoretical model for explanation of the so-called "long range proximity effect" (temperature independent and extremely large supercurrent decay length ξ^*_n≈ 10-50nm) of the HTS Josephson junctions with semiconductor oxide interlayer is proposed. It is suggested that the resonant tunneling via a large number of single localized states (LS) in the interlayer is responsible for this effect. We assume that LS are distributed uniformly in the vicinity of Fermy energy and over the interlayer and that their density is small enough for the interaction of electrons occupying different LS be negligible. The interaction of electrons at one LS is also not taken into account. We assume also that the potential barrier in the interlayer has the rectangular form with the height (V-µ) and the thickness d satisfies the inequalities : (V-µ)<<µ dT_c/(V-µ)≤α≤d, where µ is the chemical potential, m is the electron effective mass, α^-1=(2m(V-µ))^-1/2 is the effective radius of LS. The proposed model provides the explanation for whole scope of the data concerning "long range proximity effect". We believe that the model can be also applicable for interpretation of the properties of HTS single grain boundary junctions and Low-T_c structures with the gapless semiconductor interlayer.