Coherent Charge Transport in Metallic Proximity Structures

TL;DR

This paper provides a microscopic analysis of electron transport in normal diffusive conductors with proximity-induced superconductivity, revealing temperature-dependent conductance behaviors, magnetic flux effects, and consistency with recent experiments.

Contribution

It introduces a detailed microscopic model of proximity effects in diffusive conductors, highlighting nonequilibrium effects, magnetic flux tuning, and the suppression of reentrant conductance behavior.

Findings

Reentrant temperature dependence of conductance in transparent boundaries.

Aharonov-Bohm oscillations in conductance with flux-dependent amplitude.

Density of states and proximity strength tunable by magnetic flux.

Abstract

We develop a detailed microscopic analysis of electron transport in normal diffusive conductors in the presence of proximity induced superconducting correlation. 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 non-monotoneous ``reentrant'' structure. We argue that this behavior is due to nonequilibrium effects occuring in the normal metal in the presence of both superconducting correlations and the electric field there. Low transparent tunnel barriers suppress the nonequilibrium effects and destroy the reentrant behavior of the conductance. If the wire contains a loop, the conductance shows Aharonov-Bohm oscillations with the period $\Phi_0=h/2e$ as a function of the magnetic flux $\Phi$ inside the loop. The amplitude of these oscillations also demonstrates the reentrant behavior vanishing at $T=0$ and decaying 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 $\Phi$. We point out that the density of states and thus the ``strengh'' 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.