Current and noise correlations in a double dot Cooper pair beam splitter

TL;DR

This paper models a double quantum dot Cooper pair beam splitter, analyzing how energy configurations and tunneling affect current and noise correlations, revealing conditions that optimize or suppress specific quantum transport processes.

Contribution

It derives a general expression for current and noise correlations in a double quantum dot system and studies their dependence on energy levels and tunneling, highlighting conditions that favor different transport processes.

Findings

Antisymmetric energy configuration optimizes Crossed Andreev Reflection.

Symmetric energy configuration favors Elastic Cotunneling.

Direct tunneling suppresses CAR and leads to negative noise correlations.

Abstract

We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branching current and the noise crossed correlations in terms of single and two-particle Green's function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunneling, the antisymmetric case (the two levels have opposite energies with respect to the superconducting chemical potential) optimizes the Crossed Andreev Reflection (CAR) process while the symmetric case (the two levels have the same energies) favors the Elastic Cotunneling (EC) process. Switching on the direct tunneling tends to suppress the CAR process, leading to negative noise crossed correlations over the whole voltage range for large enough direct tunneling.