Josephson current through double quantum dots

We investigate how the competition between Kondo and antiferromagnetic (AF) correlations influences the Josephson current through double quantum dots (DQDs) and focus our attention on the situation where the superconducting energy gap is smaller than the Kondo temperature. The finite-U slave-boson mean-field method is adopted to treat electronic correlations. With weak AF correlation, two Kondo spin singlets yield two Andreev bound states below the Fermi level, and the low tunnelling probability through these singlet states leads to small critical Josephson current J(c). Strong AF correlation results in a singlet between the two localized spins, and only in a certain range can one bound state be found. At an intermediate point, the competition between 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 double occupancy on the bonding orbital of two dots, and no Andreev bound state is found with J(c) approaching zero.