Kondo effect in triple quantum dots

Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations, and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the interdot coupling is increased. Resulting Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.

Figure 1

(Color online) The triple quantum dot embedded between two leads.

Figure 2

(Color online) M1, M3: molecular-orbital Kondo regime with $⟨n⟩\sim 1,3$. M2: nonconductive even-occupancy state. L3: local Kondo regime with $⟨n⟩\sim 3$. TSK: two-stage Kondo regime. K2: local double Kondo regime with $⟨n⟩\sim 2$.

Figure 3

(Color online) $G∕G_0$ and $⟨n⟩$ vs ${ϵ}_d+U∕2$ (proportional to the gate voltage) for various interdot hopping $t^{″}$. Note enhanced energy scale in panels (d) and (e). Error bars of CPMC are smaller than the size of circles. For comparison, we also show the Hartree-Fock (HF) as well as $U=0$ results.

Figure 4

(Color online) Moments $⟨S_z^2⟩$ vs ${ϵ}_d+U∕2$, left panels (a1)–(e1). Spin-spin correlation functions $⟨S_{iz}{S}_{jz}⟩$ for $\left(ij\right)=\left(11\right)$, (22), (12), and (13) as calculated from the GS wave function, right panels (a2)–(e2).