Hybrid devices combining quantum dots with superconductors are important building
blocks of conventional and topological quantum-information experiments. A requirement
for the success of such experiments is to understand the various tunneling-induced
non-local interaction mechanisms that are present in the devices, namely crossed Andreev
reflection, elastic co-tunneling, and direct interdot tunneling. Here, we provide
a theoretical study of a simple device that consists of two quantum dots and a superconductor
tunnel-coupled to the dots, often called a Cooper-pair splitter. We study the three
special cases where one of the three non-local mechanisms dominates, and calculate
measurable ground-state properties, as well as the zero-bias and finite-bias differential
conductance characterizing electron transport through this device. We describe how
each non-local mechanism controls the measurable quantities, and thereby find experimental
fingerprints that allow one to identify and quantify the dominant non-local mechanism
using experimental data. Finally, we study the triplet blockade effect and the associated
negative differential conductance in the Cooper-pair splitter, and show that they
can arise regardless of the nature of the dominant non-local coupling mechanism. Our
results should facilitate the characterization of hybrid devices, and their optimization
for various quantum-information-related experiments and applications.
