Kondo Effect and Josephson Current through a Quantum Dot between Two Superconductors

TL;DR

This paper studies the supercurrent through a quantum dot between two superconductors, revealing a phase transition in the Josephson current and explaining experimental conductance crossover using numerical renormalization group methods.

Contribution

It provides a comprehensive analysis of the Josephson effect in quantum dots across all coupling regimes with numerical simulations.

Findings

Josephson current switches from π to 0 phase with increasing coupling

Ground state spin depends on phase difference at intermediate couplings

Numerical results explain experimental conductance crossover

Abstract

We investigate the supercurrent through a quantum dot for the whole range of couplings using the numerical renormalization group method. We find that the Josephson current switches abruptly from a $\pi$- to a 0-phase as the coupling increases. At intermediate couplings the total spin in the ground state depends on the phase difference between the two superconductors. Our numerical results can explain the crossover in the conductance observed experimentally by Buitelaar \textit{et al.} [Phys. Rev. Lett. \textbf{89}, 256 801 (2002)].