Nonequilibrium conductance of a three-terminal quantum dot in the Kondo regime: Perturbative renormalization group study

Motivated by recent experiments, we consider a single-electron transistor in the Kondo regime which is coupled to three leads in the presence of large bias voltages. Such a steady-state nonequilibrium system is to a large extent governed by a decoherence rate $\Gamma$ induced by the current through the dot. As the two-terminal conductance turns out to be rather insensitive to $\Gamma$, we study the conductance in a three-terminal device using a perturbative renormalization group method and calculate the characteristic splitting of the Kondo resonance. The interplay between potential biases and anisotropy in coupling to the three leads determines $\Gamma$ and the conditions for strong coupling.

Figure 1

(Color online) Upper panel shows the scaling of $g_{\omega }$ as the cutoff is decreased down to zero from $D=300T_K$, for ${\mu }_1=100T_K$, ${\mu }_2=150T_K$, ${\mu }_3=350T_K$, and $n_1=n_2=n_3$. The thinner full line shows the $g_{\omega }$ obtained if $\Gamma$ were to be $T_{*}$. Lower panel shows the renormalized $g_{\omega }(D=0)$ for ${\mu }_1=100T_K$, ${\mu }_2=225T_K$, ${\mu }_3=350T_K$ for different $n_1,n_2,n_3$ shown in the legends. In the same line style as numerical plots, also shown in both panels are the plots for $g_{\omega }$ obtained analytically (upper curves when they do not coincide).

Figure 2

(Color online) Conductance $G_{11}$ in the “two-lead spectroscopy” case $(n_1^2=0.002)$ for ${\mu }_{32}=100T_K$ and different values of $n_2^2$ and $n_3^2$. Inset shows $\Gamma$ and $T_{*}$ on a logarithm scale, as a function of $n_2^2$.

Figure 3

(Color online) Conductance $G_{11}$ in the “two-lead spectroscopy” case $(n_1^2=0.002)$ for $n_2=0.599$, $n_3=0.399$, and different values of ${\mu }_{32}$. For ${\mu }_{32}=100T_K$, the thinner full line shows $G_{11}$ if $\Gamma$ were to be $T_{*}$. The inset shows $\Gamma$ and $T_{*}$ on a logarithm scale, as a function ${\mu }_{32}$.

Figure 4

(Color online) Plots of $G_{11}$ for increasing values of $n_1^2$ (ordered by increasing peak heights) for fixed $n_2^2∕n_3^2=1.5$ and ${\mu }_{32}=100T_K$. The corner inset shows $\Gamma$ and $T_{*}$ on a logarithm scale as a function of $n_1^2$ for ${\mu }_1={\mu }_2,{\mu }_3$. The other inset shows the peak height $G_{11}({\mu }_1={\mu }_3)$ as well as the part coming only from the first term of Eq. (8) (dashed line) plotted against $n_1^2$.