Kondo effect in a side-coupled double quantum dot system embedded in a mesoscopic ring

Abstract

We study finite-size effect of the Kondo screening cloud in a double quantum dot setup via a large-N slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size L and the other dot is side coupled to the embedded dot via an antiferromagnetic spin-spin-exchange coupling with a strength K. The antiferromagnetic coupling favors local spin-singlet state and suppresses the Kondo screening. The mean-field phase diagram as a function of 1/L and K shows a crossover to the local spin-singlet ground state from the Kondo phase to occur at K < K(c) (L = 4n, 4n + 1, 4n + 3) and at K > K(c) (L = 4n + 2). The effective Kondo temperature T(k) (proptotional to inverse of the Kondo screening cloud size) shows the Kosterlitz-Thouless (KT) scaling at finite sizes for L = 4n, 4n + 2, indicating quantum transition of the KT type between the Kondo screened phase for K <= K(c) and a local spin-singlet phase for K >= K(c) in the thermodynamic limit with Kc being the critical value. The local density of states on the embedded quantum dot and the persistent current at finite sizes with different values of K are calculated in the crossover region.