Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs

We present a particle-number-conserving theory for many-body effects in mesoscopic superconducting islands connected to normal electrodes, which explicitly includes quantum fluctuations of Cooper pairs in the condensate. Beyond previous BCS mean-field descriptions, our theory can precisely treat the pairing and Coulomb interactions over a broad range of parameters by using the numerical renormalization group method. On increasing the ratio of pairing interactions to Coulomb interactions, the low-energy physics of the system evolves from the spin Kondo regime to the mixed-valence regime and eventually reaches an anisotropic charge Kondo phase, while a crossover from 1e- to 2e(-)periodic Coulomb blockade of transport is revealed at high temperatures. For weak pairing, the superconducting condensate is frozen in the local spin-flip processes but fluctuates in the virtual excitations, yielding an enhanced spin Kondo temperature. For strong pairing, massive fluctuations of Cooper pairs are crucial for establishing charge Kondo correlations whose Kondo temperature rapidly decreases with the pairing interaction. Surprisingly, a charge-exchange-induced local field may occur even at the charge degenerate point, thereby destroying the charge Kondo effect. These are demonstrated in the spectral and transport properties of the island.