Coherent charge transport in metallic proximity structures

TLDR: In this paper, the authors developed a detailed microscopic analysis of electron transport in normal diffusive conductors in the presence of proximity-induced superconducting correlations and calculated the linear conductance of the system, the profile of the electric field and the densities of states.

Abstract: We develop a detailed microscopic analysis of electron transport in normal diffusive conductors in the presence of proximity-induced superconducting correlations. We calculated the linear conductance of the system, the profile of the electric field, and the densities of states. In the case of transparent metallic boundaries the temperature-dependent conductance has a nonmonotonic ``reentrant'' structure. We argue that this behavior is due to nonequilibrium effects occurring in the normal metal in the presence of both superconducting correlations and the electric field. Low transparent tunnel barriers suppress nonequilibrium effects and destroy the reentrant behavior of the conductance. If the wire contains a loop, the conductance shows Aharonov-Bohm oscillations with a period ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/2e as a function of the magnetic flux \ensuremath{\Phi} inside the loop. The amplitude of these oscillations also demonstrates the reentrant behavior. It vanishes at T=0 and decays as 1/T at relatively large temperatures. The latter behavior is due to low-energy correlated electrons which penetrate deep into the normal metal and ``feel'' the effect of the magnetic flux \ensuremath{\Phi}. We point out that the density of states and thus the ``strength'' of the proximity effect can be tuned by the value of the flux inside the loop. Our results are fully consistent with recent experimental findings.