Excess Noise in Biased Superconducting Weak Links

TL;DR

This paper derives a general expression for excess noise in superconducting weak links, revealing a finite noise level due to fractional Andreev scattering, with specific relations between noise and excess current at high bias voltages.

Contribution

It provides a novel formalism for calculating excess noise in superconducting weak links, highlighting the role of fractional Andreev scattering and deriving explicit noise-current relations.

Findings

Finite excess noise exists in superconducting weak links due to Andreev scattering.

At high bias, noise is proportional to excess current with a specific ratio.

Both excess noise and current vanish as superconducting gap approaches zero.

Abstract

Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is derived. This formalism is applied to a current-carrying quantum channel with perfect transparency. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is fractional Andreev scattering of quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta \rightarrow 0$ both the excess noise and the excess current vanish linearly in $\Delta$, %$\propto \Delta$, their ratio being constant.