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Proximity effect on spin-dependent conductance and thermopower of correlated quantum dots

We study the electric and thermoelectric transport properties of correlated quantum dots coupled to two ferromagnetic leads and one superconducting electrode. Transport through such hybrid devices depends on the interplay of ferromagnetic-contact induced exchange field, superconducting proximity effect and correlations leading to the Kondo effect. We consider the limit of large superconducting gap. The system can be then modeled by an effective Hamiltonian with a particle-non-conserving term describing the creation and annihilation of Cooper pairs. By means of the full density-matrix numerical renormalization group method, we analyze the behavior of electrical and thermal conductances, as well as the Seebeck coefficient as a function of temperature, dot level position and the strength of the coupling to the superconductor. We show that the exchange field may be considerably affected by the superconducting proximity effect and is generally a function of Andreev bound state energies. Increasing the coupling to the superconductor may raise the Kondo temperature and partially restore the exchange-field-split Kondo resonance. The competition between ferromagnetic and superconducting proximity effects is reflected in the corresponding temperature and dot level dependence of both the linear conductance and the (spin) thermopower.