Transport through Quantum Dots in Mesoscopic Circuits

We study the transport through a quantum dot, in the Kondo Coulomb blockade valley, embedded in a mesoscopic device with finite wires. The quantization of states in the circuit that hosts the quantum dot gives rise to finite size effects. These effects make the conductance sensitive to the ratio of the Kondo screening length to the wires length and provide a way of measuring the Kondo cloud. We present results obtained with the numerical renormalization group for a wide range of physically accessible parameters.

Figure 1

(a) Mesoscopic circuit with an embedded quantum dot. (b) Conductance as a function of the QD level position for a system with infinite wires ($t_{DW}=0.14t_0$) and $U=t_0$. $T=0$ (open diamonds) $T\simeq 10T_K^0$ (filled diamonds). (c) Zero temperature conductance as a function of the QD level position for a system with finite wires ($\Delta \simeq 10T_K^0$ and $t_{CW}=0.6t_0$) and different values of ${ϵ}_W$: at-resonance (squares), off-resonance (triangles), and intermediate case ${ϵ}_W=0.4\Delta$ (circles).

Figure 2

Conductance as a function of temperature for a $\Delta \simeq T_K^0/3$ system (a) and (c), and a $\Delta \simeq 10T_K^0$ system (b) and (d). (a) and (b) At-resonance (circles) and off-resonance (squares) situations with $t_{CW}=0.5t_0$ (filled symbols), and $t_{CW}=0.6t_0$ (open symbols). (c) and (d) Conductance for different values of ${ϵ}_W/\Delta$ and $t_{CW}=0.5t_0$. The other parameters are $E_d=-0.5U$, $U=t_0$, $T_K^0\simeq 5\times {10}^{-5}{t}_0$, and $t_{DW}=0.14t_0$ [$\gamma \sim T_K^0$ for (b) and (d)]. The solid line in (a) and (b) is the conductance for an infinite wire.

Figure 3

Conductance as a function of ${ϵ}_W$ for a $\Delta \simeq 10T_K^0$ system at $T=0$ (a), $T\simeq T_K^0$ (b), and $T\simeq \Delta$ (c). ${\epsilon }_W/\Delta =0$, $\pm 0.5$ correspond to the at-resonance and off-resonance cases, respectively.

Figure 4

(a) Zero temperature transmission phase shift for a $\Delta \simeq 10T_K^0$ system. (b) Low energy detail for the at-resonance case (dotted style), off-resonance case (solid style), and an intermediate case (dashed style).