Quantum dots exhibit a variety of strongly correlated effects, e.g., when tuned to emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dots setups, the magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic whispering gallery modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the coherent RKKY-like interaction that the cavity facilitates. Specifically, we find that (i) Kondo can win and form on each dot individually, or (ii) the cavity can win and mediate between the two dots either a singlet or a novel nonlocal Kondo-like effect phase, which we call "cat Kondo". We systematically study the quantum phase transitions between the different many-body states. Our discoveries lay the foundation for the experimental observation of unconventional nonlocal magnetic impurities.Quantum dots exhibit a variety of strongly correlated effects, e.g., when tuned to emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dots setups, the magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic whispering gallery modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the coherent RKKY-like interaction that the cavity facilitates. Specifically, we find that (i) Kondo can win and form on each dot individually, or (ii) the cavity can win and mediate between the two dots either a singlet or a novel nonlocal Kondo-like effect phase, which we call "cat Kondo". We systematically study the quantum phase transitions between the different many-body states. Our discoveries lay the foundation for the experimental observation of unconventional nonlocal magnetic impurities.

arXiv:2308.16009Aug 30, 20230 citations

Quantum dots and the Kondo effect

Karyn Le Hur

NatureOct 6, 201542 citations

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

I-Ling Tsai, Chung‐Hou Chung

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 $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with ${K}_{c}$ 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.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 $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with ${K}_{c}$ 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.

arXiv:0908.0589Physical Review BMay 4, 20100 citations

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 $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with

{K}_{c}

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.