Josephson current through a nanoscale magnetic quantum dot

Abstract

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 $π$ junction behavior in a numerically exact way. Within the `magnetic' regime, $U/Γ\gg 1$ and $ε_0/Γ\leq 1$, the Josephson current is found to depend only on $Δ/T_K$, where $Δ$ 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 $Δ/T_K$.