Andreev interferometer

Phase Dependent Current Statistics in a Short-Arm Andreev Interferometer... 

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]. 

Motivated by the growing interest in high-order correlation functions, we develop in the present Paper a systematic approach to full statistics of charge transport in Andreev interferometers. We adopt several simplifying assumptions, which enables us to present an analytical solution for the CGF and, without a loss of generality, to clearly demonstrate essential features of coherent effects in the current statistics in NS structures. Our approach is based on the extended Keldysh-Green technique [13, 14], in which the CGF is determined by the equation... 

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. 

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