Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

TL;DR

This paper develops a non-perturbative theoretical framework to analyze non-equilibrium noise in multi-terminal superconducting hybrid devices, focusing on multiple Cooper pair resonances and their impact on current correlations.

Contribution

It introduces a path integral-based formalism to compute current and noise in complex superconducting quantum dot systems, applied to a novel all-superconducting Cooper pair beam splitter.

Findings

Non-zero DC currents arise from multi-Cooper pair processes in out-of-equilibrium conditions.

In the non-resonant regime, noise is negligible for quartet processes.

Resonant regimes exhibit giant Fano factors indicating enhanced noise.

Abstract

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a non-perturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the "all superconducting Cooper pair beam splitter", a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of non-local processes involving multiple Cooper pairs which ultimately lead to the presence of non-zero DC currents in an out-of-equilibrium situation. We investigate in details the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called "quartet processes", involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the non-resonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.