Suppression of the 0-π transition in a Josephson junction with parallel double-quantum-dot barriers

With the help of the numerical renormalization group method, we theoretically investigate the Josephson phase transition in a parallel junction with one quantum dot embedded in each arm. It is found that in the cases of appropriate dot levels and symmetrical dot-superconductor couplings, the Josephson phase transition will be suppressed. This is manifested as the fact that with the enhancement of the electron correlation, the supercurrent only arrives at its pi' phase but cannot enter its pi phase. Moreover, when the dot levels are detuned, one pi'-phase island appears in the phase diagram. Such a result is attributed to the interplay among the Kondo effect, RKKY effect, and the Cooper pairing correlation. We believe that this work can be helpful in understanding the special roles of the correlation mechanisms of the parallel junction in driving the Josephson phase transition.