Conductance of a quantum dot in the Kondo regime connected to dirty wires

We study the transport behavior induced by a small bias voltage through a quantum dot connected to one-channel disordered wires by means of a quantum Monte Carlo method. We model the quantum dot by the Hubbard-Anderson impurity and the wires by the one-dimensional Anderson model with diagonal disorder within a length. We present a complete description of the probability distribution function of the conductance within the Kondo regime.

Figure 1

Top panel: Mean value of the conductance $\langle G\left(T\right)\rangle$ as a function of the temperature $T$ for wires of different lengths $\ell =$ 14, 40, 100, 200, and 400. For comparison, we present in dashed lines the corresponding values for a noninteracting dot and in full line we present the conductance for a dot connected to perfect clean wires. Bottom panel: Variance ${\sigma }_2\left(T\right)$ for the same distribution as in the top panel. Inset: Relative conductance $\langle G\left(T\right)\rangle /\langle G(T=0)\rangle$. The Coulomb interaction is $U=8t$, which in the clean system corresponds to $T_K^0=0.015t$. The disorder strength is $W=t/2$, the gate voltage is $V_g=U/2$, and the chemical potential is $\mu =0$. The mean free path of these wires in the noninteracting limit is ${\xi }_{\mathrm{mfp}}=144$.

Figure 2

Variance for the interacting [${\sigma }_2\left(T\right)$] and noninteracting [${\sigma }_2^0\left(T\right)$] system as a function of the length $\ell$ for wires at low temperature $T\approx T_K^0/3\text{and}2T_K^0/3$. Other parameters are the same as in Fig. 1.

Figure 3

PDF for the full $P\left(G\right)$ (full line) and noninteracting $P\left(G_0\right)$ (dash-dotted line) conductance. Left, middle, and right panels correspond to $T=T_K^0/3$, $T=1.33T_K^0$, and $T\approx 4.5T_K^0$, respectively. On each panel, three different lengths of the dirty wires $\ell =14,40,\text{and}100$ are shown. Other parameters are the same as in Figs. 1 and 2.

Figure 4

PDF for the LDS, $P\left({\rho }_{\sigma }\left(0\right)\right)$ at $T=T_K^0/3$ (left panel) and $T\approx 4.5T_K^0$ (right panel), of an interacting quantum dot in the Kondo regime, corresponding to three different lengths of the dirty wires $\ell =14,40,\text{and}100$. For comparison, we also show in dash-dotted lines the function $P\left({\rho }^0\left(0\right)\right)$ corresponding to the noninteracting system. For the lower temperature, we also show in dashed lines the PDF corresponding to the Fermi-liquid description. Other parameters are the same as in Figs. 1 and 2.