Kondo effect in a side-coupled double-quantum-dot system embedded in a mesoscopic ring
Abstract
We study the 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 anti-ferromagnetic spin-spin exchange coupling with the strength K. The antiferromagnetic coupling favors the local spin-singlet and suppresses the Kondo screening. The effective Kondo temperature Tk (proptotional to the inverse of the Kondo screening cloud size) shows the Kosterlitz--Thouless (KT) scaling at finite sizes, indicating the quantum transition of the KT type between the Kondo screened phase for K < Kc and the local spin-singlet phase for K > Kc in the thermodynamic limit with Kc being the critical value. The mean-field phase diagram as a function of 1/L and K shows a crossover between Kondo and local spin-singlet ground states for K < Kc (L=4n, 4n+1, 4n+3) and for K>Kc (L=4n+2). To look into the crossover region more closely, the local density of states on the quantum dot and the persistent current at finite sizes with different values of K are also calculated.