Interplay between the Mesoscopic Stoner and Kondo Effects in Quantum Dots

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-$\frac{1}{2}$ Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling $\tilde{J}$, where $\tilde{J}=1$ denotes the bulk Stoner transition. We show that as $\tilde{J}$ approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.

Figure 1

The variation of $p$, ${\Delta }_K$, and the ground state energy with $\tilde{J}$ for ${\Delta }_{K0}=100\delta$. The solid line represents the ground state energy of regime I, while the dashed line represents that of regime II. Their crossing, demarcated by the solid vertical line, is the transition at ${\tilde{J}}^{*}=0.9975$. Note that ${\Delta }_K$ continuously increases in regime I and that there is a large jump in $p$ at the transition.

Figure 2

The variation of $p$, ${\Delta }_K$, and the ground state energy with $E_Z$ for ${\Delta }_{K0}=100\delta$ and $\tilde{J}=0.99$. Their values at $E_Z=0$ have been subtracted out and are $p(0)=34$, ${\Delta }_K(0)=109.5$, and $E_{\mathrm{gs}}(0)=-81.67$. Note that $E_Z$ is in units of $\delta$, and even for $E_Z=0.5\delta$ there is a 10% enhancement of ${\Delta }_K$.