Coulomb Effects on Electron Transport and Shot Noise in Hybrid Normal-Superconducting Metallic Structures

TL;DR

This paper investigates how electron-electron interactions influence Andreev current and shot noise in diffusive normal-superconductor structures, revealing a dimensionality-dependent reduction at low energies and a power-law correction at higher voltages.

Contribution

It provides a detailed analysis of Coulomb interaction effects on transport and noise in hybrid structures, highlighting the dependence on system dimensionality and energy scales.

Findings

Coulomb interactions reduce Andreev current and noise below the Thouless energy.

The reduction factor depends on the number of channels and conductance, especially in quasi-1D systems.

At energies above the Thouless energy, corrections follow a power-law voltage dependence.

Abstract

We analyze the effect of electron-electron interactions on Andreev current and shot noise in diffusive hybrid structures composed of a normal metal attached to a superconductor via a weakly transmitting interface. We demonstrate that at voltages/temperatures below the Thouless energy of a normal metal Coulomb interaction yields a reduction of both Andreev current and its noise by a constant factor which essentially depends on the system dimensionality. For quasi-1d structures this factor is $\sim N_{\rm Ch}^{8/g}$, where $N_{\rm Ch}$ and $g$ are respectively the number of conducting channels and dimensionless conductance of a normal metal. At voltages above the Thouless energy the interaction correction to Andreev current and shot noise acquires an additional voltage dependence which turns out to be a power-law in the quasi-1d limit.