Presence of asymmetric noise in multiterminal chaotic cavities

This work deals with chaotic quantum dot connected to two and four leads. We use standard diagrammatic procedure to integrate on the unitary group, to study the main term in the semiclassical expansion of the noise in the three pure Wigner-Dyson ensembles at finite frequency and temperature, in the noninteracting and interacting regimes. We investigate several limits, related to the temperature and the potential difference in the leads, in the presence of a capacitive environment. At the thermal crossover regime, we obtain general expressions described in terms of parameters that can be controlled experimentally. As an interesting result, we show the appearance of asymmetries in the noise, controlled by the topology of the cavity and the number of open channels in the corresponding terminals.

Figure 1

Illustration of the chaotic quantum dot connected to four leads, with $C$ standing for the capacitive environment. We use $V_{12}=V_1-V_2$ and $V_{34}=V_3-V_4$ to identify the difference of potentials between the leads 1 and 2, and 3 and 4, respectively.

Figure 2

The upper panel shows the noise in the regime of finite frequency with capacitive interaction, in terms of $\beta e{V}_{12}$. The lower panel shows the corresponding second derivative, and the inset depicts its behavior in the case of two terminals. Here we have set $\beta e{V}_{34}=10$, $\beta \hslash w=0.3$, and $\tau /\hslash \beta =1$.

Figure 3

The upper panel shows the noise in the regime of finite frequency with capacitive interaction, in terms of $\beta e{V}_{34}$. The lower panel shows the corresponding second derivative. Here we have set $\beta e{V}_{12}=10$, $\beta \hslash w=0.3$, and $\tau /\hslash \beta =1$.

Figure 4

The upper panel shows the noise in the regime of finite frequency with capacitive interaction, in terms of $\beta e{V}_{34}$. The lower panel shows the corresponding second derivative. Here we have set $\beta e{V}_{12}=10$, $\beta \hslash w=0.3$, and $\tau /\hslash \beta =1$.

Figure 5

Similar plots of the noise $S_{21}$ and its second derivative. Here we have set $N_1=15$, $N_2=40$, $N_3=50$, $N_4=25$, $\beta \hslash w=0.3$, and $\tau /\hslash \beta =1$.

Figure 6

Plots of the noise $S_{21}$ and its second derivative. We note a suppression in the peaks of the second derivative of the noise due to the increasing of the frequency. Here we have set $N_1=15$, $N_2=40$, $N_3=50$, $N_4=25$, $\beta e{V}_{34}=10$, and $\tau /\hslash \beta =1$.

Figure 7

Noise in the regime of finite frequency with capacitive interaction, in terms of the number of open channels in terminals 2 and 3. Here we have set $\beta e{V}_{12}=10$, $\beta e{V}_{34}=15$, $\beta \hslash w=0.3$, and $\tau /\hslash \beta =1$.