Coulomb drag effect induced by the third cumulant of current

The Coulomb drag effect arises due to electron-electron interactions when two metallic conductors are placed in close vicinity to each other. It manifests itself as a charge current or voltage drop induced in one of the conductors, if the current flows through the second one. Often it can be interpreted as an effect of rectification of the nonequilibrium quantum noise of current. Here, we investigate the Coulomb drag effect in mesoscopic electrical circuits and show that it can be mediated by classical fluctuations of the circuit collective mode. Moreover, by considering this phenomenon in the context of the full counting statistics of charge transport, we demonstrate that not only the noise power but also the third cumulant of current may contribute to the drag current. We discuss the situations where this contribution becomes dominant.

Figure 1

The simplified electrical circuit for studying the Coulomb drag effect is shown. It consists of two parts: the drive circuit, containing a quantum conductor with the resistance $R_S$, which is the source of the current noise, and the drag circuit, containing a tunnel junction with the resistance $R_T$ and capacitance $C_T$, which serves as a detector of noise. The voltage bias $\mathrm{\Delta }V=V_d-V_L$, applied to the quantum conductor, causes the average current $\langle I\rangle$ and nonequilibrium current fluctuations $\delta I$ through it. The circuit responds by the voltage fluctuations $\delta V$ across the tunnel junction at the characteristic frequency ${\omega }_c=1/\left(RC\right)$, where the circuit resistance is defined as $R^{-1}=R_L^{-1}+R_S^{-1}$, and the total capacitance is given by $C=C_L+C_T$. These fluctuations cause the drag current $I_D$ through the tunneling junction, which is calculated perturbatively in small $1/R_T$. The extra potential $V_L$ is applied to tune the circuit to the point $V=0$ in order to cancel the average bias across the junction. An example of an open circuit for the drag effect detection is discussed in Sec. 5.

Figure 2

An example of an open circuit for studying the Coulomb drag effect is shown. Compared to the circuit shown in Fig. 1, an extra capacitor $C_D$ is added in order to filter out the DC component of the voltage $V$, as well as the low-frequency part of fluctuations $\delta V$. The high-frequency part of fluctuations propagates towards the detector part of the circuit and causes the drag voltage $U_D$ across the tunnel junction. One can use the additional shunt resistor $R_D$ to controllably access the nonlinear regime of the tunnel junction. The relation between the drag voltage $U_D$ in the open circuit and the drag current $I_D$ in the circuit shown in Fig. 1 is studied in Sec. 5.