Transport through a superconductor-interacting normal metal junction: a phenomenological description

TL;DR

This paper introduces a simple phenomenological model for electronic transport at a normal metal/superconductor interface that incorporates electron-electron interactions via an energy-dependent transmission, capturing key experimental and theoretical features.

Contribution

It presents a novel, simplified approach to model transport with interactions, bridging the gap between complex theories and experimental data.

Findings

Reproduces qualitative results of more complex theories

Captures crossover from Andreev to tunneling regimes

Aligns with experimental observations

Abstract

We propose a phenomenological description of electronic transport through a normal metal/superconductor interface of arbitrary transparency, which accounts for the presence of electron-electron interaction in the normal metal. The effect of interactions is included through an energy-dependent transmission probability that is inserted in the expression for the current-voltage characteristics of a non-interacting system. This results in a crossover from the Andreev to the tunneling limit as a function of the energy at which transport is probed. The proposed description reproduces qualitatively the results obtained with formally correct theories as well as experimental observations. In view of its simplicity, we expect our approach to be of use for the interpretation of future experiments.