Josephson current through a nanoscale magnetic quantum dot

We present theoretical results for the equilibrium Josephson current through an Anderson dot tuned into the magnetic regime, using Hirsch-Fye Monte Carlo simulations covering the complete crossover from Kondo-dominated physics to pi junction behavior in a numerically exact way. Within the magnetic regime, U/Gammamuch greater than1 and epsilon(0)/Gammaless than or equal to1, the Josephson current is found to depend only on Delta/T-K, where Delta is the BCS gap and T-K the Kondo temperature. The junction behavior can be classified into four different quantum phases. We describe these behaviors, specify the associated three transition points, and identify a local minimum in the critical current of the junction as a function of Delta/T-K.