Abstract
We investigate how the competition between Kondo and antiferromagnetic (AF) correlationsinfluences the Josephson current through double quantum dots (DQDs) and focus our attention onthe situation where the superconducting energy gap is smaller than the Kondo temperature. Thefinite-U slave-boson mean-field method is adopted to treat electronic correlations. With weak AFcorrelation, two Kondo spin singlets yield two Andreev bound states below the Fermi level, andthe low tunnelling probability through these singlet states leads to small critical Josephson currentJc. Strong AF correlation results in a singlet between the two localized spins, and only in acertain range can one bound state be found. At an intermediate point, the competitionbetween the Kondo and AF correlations leads to a peak in the critical Josephson current,where just one bound state is formed in the gap. The strong parity splitting causes the doubleoccupancy on the bonding orbital of two dots, and no Andreev bound state is found withJc approaching zero.
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