Figure 1

A proposed realization of the two-channel Kondo (2CK) model. Two noninteracting leads ($L$ and $R$) and a large dot $m$ are attached to a single-level small dot $d$. If dot $d$ is occupied by a single electron, it can flip its spin by virtually hopping the electron onto either dot $m$ or the leads, and then returning an electron with opposite spin to dot $d$. Dot $m$ and the leads thus serve as the two distinct screening channels required to produce the 2CK effect. Crucially, when $kT$ is smaller than the charging energy of dot $m$, Coulomb blockade blocks transfer of electrons between the leads and dot $m$. Fine-tuning of the voltage ${\mathcal{V}}_m$ (and/or ${\mathcal{V}}_d$) can equalize the coupling to the two channels, stabilizing the 2CK fixed point.Reuse & Permissions

Figure 2

The number of electrons on dots $m$ and $d$ are functions of the gate voltages ${\mathcal{V}}_m$ and ${\mathcal{V}}_d$. Within the central hexagon, dot $d$ is singly occupied, a prerequisite for observation of the Kondo effect. Curves superimposed on this hexagon (“2CK lines”) map where in the ${\mathcal{V}}_m,{\mathcal{V}}_d$ plane the two-channel Kondo (2CK) effect is realized for two different values of the coupling ratio $\gamma \equiv {\Gamma }_m/{\Gamma }_{\psi }$—each value gives rise to a pair of disjoint curves. As illustrated for $\gamma =1.08$ (dashed lines), these two curves divide the hexagon into three regions with distinct low-temperature fixed points. On the curves, the 2CK effect is realized and the deviation of the interlead differential conductance from its $T\to 0$, ${\mathcal{V}}_{LR}\to 0$ limit $G(0,0)$ is $\propto \sqrt{\max (T,{\mathcal{V}}_{LR})}$ [Eq. (4a)]. In the shaded regions at the top left and bottom right, dot $m$ “wins,” forming an exclusive 1CK resonance with dot $d$, and driving $G(T,{\mathcal{V}}_{LR})$ close to zero [Eq. (4b)]. By contrast, in the large unshaded region, leads $L$ and $R$ “win” giving rise to familiar Fermi-liquid behavior $G(0,0)-G(T,{\mathcal{V}}_{LR})\propto [\max (T,{\mathcal{V}}_{LR}){]}^2$ [Eq. (4c)]. With increasing $\gamma$, the regions where dot $m$ wins grow and merge, while the region where the leads win shrinks and splits.Reuse & Permissions