Andreev wires

Single Particle Transport in Disordered Andreev Wires... 

Summary. We study how the single-electron transport in clean Andreev wires is affected by a weak disorder introduced by impurity scattering. The transport has two contributions, one is the Andreev diffusion inversely proportional to the mean free path i and the other is the drift along the transverse modes that increases with increasing . This behavior leads to a peculiar re-entrant localization as a function of the mean free path. 

Usually, the electronic thermal conductance re can be calculated from the Wiedemann - Franz law, re TG/e2. However, as shown in Ref. [8, 9] for the ballistic limit f > d, this law gives a wrong result for Andreev wires if one uses an expression for G obtained for a wire surrounded by an insulator. Andreev processes strongly suppress the single electron transport for all quasiparticle trajectories except for those which have momenta almost parallel to the wire thus avoiding Andreev reflection at the walls. The resulting expression for the thermal conductance... 

Here we report how the single electron transport in Andreev wires at low temperatures T weak disorder introduced by impurity scattering assuming that inelastic processes are negligible. The Andreev wire is clean in the sense that the mean free path is much longer than the wire diameter, 3> a. 

The total single-particle transport of a clean Andreev wire contains two contributions one is the Andreev diffusion decreasing as 1 and the other... 

Fig. 1. A model of Andreev interferometer. A diffusive wire of the length L connects a normal reservoir (N) and short SNS junction of the length d magnetic flux (T> threads a superconducting loop (S) of the interferometer.

In the Andreev interferometers (see Fig. 1), the phase relations between the electron and hole wavefunctions in the normal wire can be controlled by the magnetic flux enclosed by a superconducting loop, which results in the periodic dependence of transport characteristics of the interferometer on the superconducting phase difference across the SNS junction. Initially, the oscillations of the conductance were investigated both experimentally (see a review in Ref. [11]) and theoretically [12], and, more recently, the oscillations in the current noise were reported [10]. 

Furthermore, if d is much smaller than the coherence length = yftP/A, these Green functions take the BCS form, with the phase-dependent proximity gap A,p = A cos(c/)/2) [18]. This results in the BCS-like singularity at the gap edge in the density of states (DOS) of the normal wire and suppression of the DOS at E < A,/,. Within such model, the problem of current statistics in the Andreev interferometer reduces to the calculation of the CGF for an NS junction with the effective order parameter A,p in the superconducting reservoir. 

The counter-intuitive behavior of the single-particle conductance Eq. (3) which increases with decreasing was first predicted by Andreev [10]. Comparing Eq. (3) with the ballistic ( d) expression Eq. (1) we see that disorder with d stimulates the single-particle transport by opening of new single-particle conducting modes that are blocked by Andreev reflections in the ballistic limit. The conductance reaches its maximum when the mean free path decreases down to a, after which the distinction between the usual and the Andreev diffusion is lost and Eq. (3) transforms into Eq. (4) for a dirty wire (see [11] for the particular case of vortex lines). 

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