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Kondo impurity between superconducting and metallic reservoir: the flow equation approach

It is well established that a correlated quantum impurity embedded in a metallic host can form the many-body Kondo state with itinerant electrons due to the effective antiferromagnetic coupling. Such effect is manifested spectroscopically by a narrow Abrikosov-Suhl peak appearing at the Fermi level below a characteristic temperature T_K. Recent experiments using nanoscopic heterojunctions where the correlated quantum impurities (dots) are coupled to superconducting reservoirs revealed that the Kondo-type correlations are substantially weaker because: i) the single-particle states of superconductors are depleted around the Fermi level and ii) the on-dot pairing (proximity effect) competes with the spin ordering. Within the Anderson impurity scenario we study here influence of such induced on-dot paring on the exchange interaction adopting the continuous unitary transformation, which goes beyond the perturbative framework. Our analytical and numerical results show strong detrimental influence of the electron pairing on the effective antiferromagnetic coupling thereby suppressing the Kondo temperature in agreement with the experimental observations.