Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
arXiv:2509.03908 · doi:10.1103/PhysRevB.106.075117
Abstract
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 an unprecedentedly broad range of parameters by using the numerical renormalization group method. On increasing the ratio of pairing to Coulomb interactions, the low-energy physics of the system evolves from the spin Kondo to mixed valence regimes and eventually reaches an anisotropic charge Kondo phase, while a crossover from - to -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.
16 pages, 3 figures
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