Electron transport and current fluctuations in short coherent conductors

Employing a real-time effective action formalism we analyze electron transport and current fluctuations in comparatively short coherent conductors in the presence of electron-electron interactions. We demonstrate that, while Coulomb interaction tends to suppress electron transport, it may strongly enhance shot noise in scatterers with highly transparent conducting channels. This effect of excess noise is governed by the Coulomb gap observed in the current-voltage characteristics of such scatterers. We also analyze the frequency dispersion of higher current cumulants. Our results illustrate a direct relation between electron-electron interaction effects and current fluctuations in disordered mesoscopic conductors.

Figure 1

Third cumulant of the current operator ${\mathcal{S}}_3$ at zero temperature as a function of frequencies ${\omega }_1$ and ${\omega }_2$. Note that ${\mathcal{S}}_3({\omega }_1,{\omega }_2)$ changes its sign with increasing frequencies and flattens off at $\mid {\omega }_1\mid$, $\mid {\omega }_2\mid >eV$.

Figure 2

Fifth current cumulant ${\mathcal{S}}_5$ at $T=0$. Two frequencies are fixed, ${\omega }_1={\omega }_2=-5eV$, while two others, ${\omega }_3$ and ${\omega }_4$ are varied.

Figure 3

Frequency dependence of the noise power spectrum (solid line) at $T=0$ and in the presence of interactions. For comparison the noise spectrum in the absence of interactions is shown by the dashed line. Both curves are plotted for $N_{\mathrm{ch}}=1$, $\mathcal{R}=0.1$, $g_S=2$, and $V=e∕2C$.

Figure 4

The zero-frequency shot noise power spectrum ${\mathcal{S}}_I\left(0\right)$ normalized by the value $e^2\mathcal{R}∕RC$ as a function of voltage $V$ at $T=0$ for $N_{\mathrm{ch}}=1$ and small $\mathcal{R}⪡1$. The conductance $g_S$ effectively controls the interaction strength, i.e., at small $g_S$ the interaction is strong, while it tends to zero in the limit $g_S\to \infty$. The interaction-induced excess noise is clearly observed even at rather large values of $g_S$. Our results remain formally applicable at nonzero voltages $eV\gtrsim E^{*}$, while ${\mathcal{S}}_I\left(0\right)$ should always vanish in the zero-voltage limit $V=0$. However, the corresponding crossover region may become extremely narrow for $g\to 2$ and very small $\mathcal{R}$; cf. the top curve.