Fermi-Liquid versus Non-Fermi-Liquid Behavior in Triple Quantum Dots

We study the effect of electron hopping in triple quantum dots modeled by the three-impurity Anderson model. We determine the range of hopping parameters where the system exhibits the two-channel Kondo effect and has non-Fermi-liquid properties in a wide temperature interval. As this interval is entered from above, the conductance through the side dots increases to a half of the conductance quantum, while the conductance through the system remains small. At lower temperatures the conductance through the system increases to the unitary limit as the system crosses over to the Fermi-liquid ground state. Measuring the differential conductance in a three-terminal configuration provides an experimental probe into the NFL behavior.

Figure 1

Charge fluctuations and spin-spin correlations of model I (lines without symbols) and model II (lines with symbols) as a function of the interdot coupling $t$ (for model I) or corresponding $J=4t^2/U$ (for model II). The MO regime is characterized by large on-site charge fluctuations, the AFM regime by negative spin correlations of neighboring spins 1–2 and positive correlation of spins 1–3, and the TSK regime by vanishing spin correlations.

Figure 2

Impurity susceptibility and entropy for model I (full lines) and model II (dashed line) with $J=4t^2/U$. Lozenges ◆ are a fit to Bethe-Ansatz results for one-channel Kondo model (multiplied by two and shifted by $1/4$) and squares ■ are a fit to NRG results for 2CK model. Inset: $T_K^{(2)}=a{T}_K^{(1)}\exp (-b{T}_K^{(1)}/J)$ scaling of the second Kondo temperature of model I. $a=0.97$, $b=4.4$, $T_K^{(1)}/D\approx {1.010}^{-5}$.

Figure 3

Crossover scales of models I and II as functions of the interdot coupling. The magnetic screening temperature $T_{\mathrm{scr}}$ is defined by $T_{\mathrm{scr}}\chi (T_{\mathrm{scr}})/(g{\mu }_B{)}^2=0.07$; it is equal to the Kondo temperature when screening is due to the single-channel Kondo effect. $T_{\Delta }$ is here defined as $s_{\mathrm{imp}}(T_{\Delta })/k_B=\ln 2/4$.

Figure 4

NRG eigenvalue flow of model I ($\Lambda =2$, $z=1$) in the crossover regime (below) and the corresponding impurity entropy (above). The states are classified according to the total isospin and total spin quantum numbers, ($I$, $S$). Black full strips correspond to FL spectrum. Gray (red online) hatched strips are at energies (after rescaling by 1.296) $\frac{1}{8}$, $\frac{1}{2}$, $\frac{5}{8}$, 1 [9].

Figure 5

Dynamic properties of model I in the AFM (dashed lines) and in the crossover regime (full lines). Upper panel: on-site spectral function $A_1(\omega )$ of the left dot. Lower panel: out-of-diagonal spectral function $A_{13}(\omega )$ squared. Temperature $T_{\Delta }^{*}$ is of order $T_{\Delta }$, $T_K^{*}$ is of order $T_{\mathrm{scr}}$.