Competition between Nagaoka ferromagnetism and superconducting pairing in hybrid quantum dots

We investigate the interplay between Nagaoka ferromagnetism and superconducting pairing correlations in a 2×22 \times 22×2 quantum dot array coupled to an s-wave superconductor. Focusing on the subgap regime, we map out the system's phase diagram and show that the presence of superconducting correlations strongly modifies the Nagaoka ferromagnetic state. Depending on the relative strengths of direct and crossed Andreev reflections, this ferromagnetism can be entirely suppressed. We identify the critical value of the induced on-dot pairing potential at which this suppression occurs and provide analytical expressions in the limit of strong Coulomb interactions. Furthermore, we explore how the competition between Nagaoka ferromagnetism and superconductivity manifests in transport properties. Using the real-time diagrammatic technique, we calculate the nonequilibrium current and differential conductance for a plaquette weakly coupled to an external probe lead. We also analyze the case of strong correlations by means of numerical renormalization group method. Our analysis reveals how Nagaoka ferromagnetism influences the Andreev current and conductance, and we demonstrate the occurrence of a spin-quintuplet blockade in the Andreev transport.