Frequency-dependent third cumulant of current in diffusive conductors

We calculate the frequency dispersion of the third cumulant of current in diffusive-metal contacts. The cumulant exhibits a dispersion at the inverse time of diffusion across the contact, which is typically much smaller than the inverse $RC$ time. This dispersion is much more pronounced in the case of strong electron-electron scattering than in the case of purely elastic scattering because of a different symmetry of the relevant second-order correlation functions.

Figure 1

The geometry of the system considered. White areas show the diffusive metal and dark areas the insulator.

Figure 2

The coordinate dependence of the zero-frequency correlator ${⟨\delta \varphi \left(x\right)\delta I⟩}_{\omega }$ normalized to $eV$ for the elastic case (solid line) and the hot-electron regime (dashed line).

Figure 3

The real part of the ratio $P\left(\omega \right)∕\left(e^{2}I\right)$ vs normalized frequency $\omega {\tau }_D$ $\left({\tau }_D=L^2∕D\right)$ for purely elastic scattering at $eV⪢T$ (solid line), hot-electron regime at $eV⪢T$ (dashed line), purely elastic scattering at $eV⪡T$ (dotted line), and hot-electron regime at $eV⪡T$ (dash-dotted line). Inset: charged and uncharged fluctuations of the distribution function $f$. Charged fluctuations have a short relaxation time and contribute to fluctuations of current $\delta I$. Uncharged fluctuations do not contribute to $\delta I$ directly but affect the intensity of noise sources. They decay only via slow diffusion and result in the low-frequency dispersion of the third cumulant.

Figure 4

The imaginary part of the ratio $P\left(\omega \right)∕\left(e^{2}I\right)$ vs normalized frequency $\omega {\tau }_D$ $\left({\tau }_D=L^2∕D\right)$ for purely elastic scattering at $eV⪢T$ (solid line), hot-electron regime at $eV⪢T$ (dashed line), and purely elastic scattering at $eV⪡T$ (dotted line), and hot-electron regime at $eV⪡T$ (dash-dotted line).