Current correlations in the interacting Cooper-pair beam-splitter

TL;DR

This paper develops a theoretical approach to compute currents and their correlations in interacting multiterminal mesoscopic systems, specifically applied to a Cooper-pair beam-splitter setup with quantum dots, revealing how weak Coulomb interactions influence current correlations.

Contribution

The paper introduces a self-consistent Green's function formalism for calculating currents and correlations in interacting quantum dot systems connected to superconducting and normal leads, including Coulomb interactions.

Findings

Weak Coulomb repulsion favors positive current cross correlations.

The formalism accounts for local interactions and dot tunneling effects.

Application to a Cooper-pair beam-splitter model demonstrates the method's effectiveness.

Abstract

We propose an approach allowing the computation of currents and their correlations in interacting multiterminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. The formalism relies on the expression of branching currents and noise crossed correlations in terms of one- and two-particle Green's functions for the dots electrons, which are then evaluated self-consistently within a conserving approximation. We then apply this to the Cooper-pair beam-splitter setup recently proposed [L. Hofstetter et al. Nature (London) 461 960 (2009); Phys. Rev. Lett. 107 136801 (2011); L. G. Herrmann et al. Phys. Rev. Lett. 104 026801 (2010)], which we model as a double quantum dot with weak interactions, connected to a superconducting lead and two normal ones. Our method not only enables us to take into account a local repulsive interaction on the dots, but also to study its competition with the direct tunneling between dots. Our results suggest that even a weak Coulomb repulsion tends to favor positive current cross correlations in the antisymmetric regime (where the dots have opposite energies with respect to the superconducting chemical potential).