Mesoscopic proximity effect probed through superconducting tunneling contacts

Abstract

We investigate the properties of complex mesoscopic superconducting-normal hybrid devices, Andreev Interferometers in the case where the current is probed through a superconducting tunneling contact whereas the proximity effect is generated by a transparent SN interface. We show within the quasiclassical Green'sfunctions technique, how the fundamental SNIS element of such structures can be mapped onto an effective SЈIS junction, where SЈ is the proximized material with an effective energy gap E g Ͻ⌬. The conductance through such a sample at Tϭ0 vanishes if VϽ⌬ϩE g , whereas at TϾ0 the conductance shows a peak at V ϭ⌬ϪE g . We propose the Andreev interferometer, where E g can be tuned by an external phase and displays maxima at 0 mod 2 and minima at mod 2. This leads to peculiar current-phase relations, which depart from a zero-phase maximum or minimum depending on the bias voltage and can even show intermediate extreme at VϷ⌬. We propose an experiment to verify our predictions and show how our results are consistent with recent, unexplained experimental results.The proximity effect, although already known for many decades ͑see, e.g., Ref. 1͒, has recently attracted renewed scientific interest in the context of mesoscopic normalsuperconducting hybrid structures, which are now experimentally acessible due to progress in nanofabrication and measurement support technology.2-4 Departing from the properties of single junction and the nonmonotonic diffusion conductance of SN wires, the interest turned to the possibility of tuning the conductance by an external phase or a loop in the normal part. On the other hand, if probed through tunneling contacts 5 the conductance is controlled by the DOS and the induced minigap, 6,7 which can also be controlled by a phase 8 and hence opens another channel for phase controlled conductance of a different sign.9,10 If a system contains more than one superconducting terminal, a supercurrent can flow. The situation becomes more difficult and, in particular, time dependent, if nonequilibrium is created by applying an external voltage parallel to the junction. This latter situation is substantially simplified, if one of the contacts is separated from the rest of the structure by a tunneling barrier. In that case, the voltage and phase drop is concentrated at the barrier and the problem is essentially split into two parts: The time dependence of the phase at the contact and the proximity effect, which determines the superconducting properties at the normal side of the contact, within the normal metal. In that case, the physics should be basically identical to the case of an SЈIS junction, where the properties of the ''superconductor'' SЈ are entirely controlled by the proximity effect, i.e., we expect a gap of size E g Ͻ⌬ where, if the junction is long, dӷ 0 E g ϰE Th ϭD/d 2 , the Thouless energy. Hence we will expect the known 11

Crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions

“…where δ∆ * ∼ ∆(κ∆/ǫ T h ) 2/3 . Equations (14), (15) and (17) complement our qualitative considerations presented at the beginning of this paper. At this point, let us discuss the obtained results and limits of their applicability.…”

“…22 The purpose of this work is to point out a subtle feature of the crossover in the local density of states of mesoscopic SNS junctions. The latter was seen in some early and recent studies, 8,11,12,14,15 however, neither emphasized nor theoretically addressed.To this end, consider normal wire (N) of length L and width W located between two superconductive electrodes (S). In what follows, we concentrate on diffusive quasi-onedimensional geometry and the short wire limit L ≪ ξ, where ξ = √ D S /∆ is superconductive coherence length, with D S as the diffusion coefficient in the superconductor and ∆ as the energy gap (hereafter, = 1).…”

“…For quasi-one-dimensional geometry discussed here, a factor of ξ S ∝ 1 1−ε 1/4 gained after x integration exactly compensates the dip in ρ(ǫ, x) at ǫ ∼ ∆ [see Eqs. (15) and (17b)], leading to the finite value ρ(ǫ=∆) ∼ ǫ T h /∆. For d > 1, the density of states at superconductive gap edge ǫ ∼ ∆ should diverge as a certain power-law ρ(ǫ) ∼ (ǫ − ∆) −p for p > 0.…”

“…Although ρ(ǫ, x) was analytically calculated at SN interfaces only it turns out that its energy dependence is generic for any x ∈ [−L/2, L/2] and given by Eqs. (14), (15) and (17). The exact numerical prefactor, however, is x dependent and should be determined numerically.…”

Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types

“…However, recently Levchenko reported the finding of a dip in the LDOS close to the gap edge for short diffusive Josephson junctions with ideal contacts [26]. Actually, this dip was already seen in former publications [5,[27][28][29][30][31], however, no special attention was paid to it. In a previous work [32] we found the peculiar result that the suppression of the LDOS at is not limited to a dip, but a secondary gap of finite width appears for a diffusive system or chaotic cavity with the normal region connected through ballistic contacts to the superconductors.…”