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

TL;DR

This paper investigates how the finite size of a mesoscopic ring affects the Kondo screening cloud in a double-quantum-dot system, revealing a quantum phase transition characterized by Kosterlitz--Thouless scaling.

Contribution

It introduces a large-N slave-boson mean-field approach to analyze the finite size effects and identifies a KT-type transition between Kondo and spin-singlet phases.

Findings

Kondo temperature exhibits KT scaling at finite sizes.

Phase diagram shows crossover between Kondo and spin-singlet states.

Local density of states and persistent current reveal the nature of the transition.

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 T_k (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 < K_c and the local spin-singlet phase for K > K_c in the thermodynamic limit with K_c 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 < K_c (L=4n, 4n+1, 4n+3) and for K>K_c (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.