Mixed-valence transition in a quantum dot coupled to superconducting and spin-polarized leads

We consider a quantum dot coupled to both superconducting and spin-polarized electrodes, and we study the triad interplay of the Kondo effect, superconductivity, and ferromagnetism, any two of which compete with and suppress each other. We find that the interplay leads to a mixed-valence quantum phase transition, which for other typical systems is merely a crossover rather than a true transition. At the transition, the system changes from a spin-doublet to -singlet state. The singlet phase is adiabatically connected (through crossovers) to the so-called "charge Kondo state" and to the superconducting state. We analyze in detail the physical characteristics of different states, and we propose that the measurement of the cross-current correlation and the charge relaxation resistance can clearly distinguish between them.