Noise properties and ac conductance of mesoscopic diffusive conductors with screening

TL;DR

This paper develops a theory for non-equilibrium noise and high-frequency conductance in mesoscopic diffusive conductors with screening, revealing how these properties depend on geometry, frequency, and electron-electron interactions.

Contribution

It provides detailed analytical results for shot noise and conductance in specific geometries, highlighting the impact of screening and electron-electron scattering on frequency-dependent noise behavior.

Findings

High-frequency shot noise approaches a finite value between 2eI/3 and 2eI for short systems.

For long systems, shot noise grows as frequency^{1/4} at zero temperature.

Temperature affects shot noise linearly or quadratically depending on system size and scattering length.

Abstract

A theory of non-equilibrium (``shot'') noise and high frequency conductance in diffusive mesoscopic conductors with screening is presented. Detailed results are obtained for two simple geometries, for both large and short electron-electron scattering length $l_{ee}$, at frequencies of the order of the inverse Thouless time $1/\tau_T$. The conductance and the noise are found to exhibit significant frequency dependence. For $L \ll l_{ee}$, the high-frequency ($\omega\tau_T \gg 1$) shot noise spectral density $S_I(\omega)$ approaches a finite value between $2eI/3$ and $2eI$, depending on the screening properties of the system, with temperature corrections to $S_I(\omega)$ being linear in $T$. However, when $L \gg l_{ee}$, $S_I(\omega)$ grows as $\omega^{1/4}$ (at T=0), is not upper-bound by $2eI$, and has a temperature-dependent component quadratic in $T$. As a result, measurements of $S_I(\omega, T)$ can be utilized as a probe of the strength of electron-electron scattering.