Semiclassical theory of shot noise in mesoscopic conductors

TL;DR

This paper develops a semiclassical framework to analyze shot noise in mesoscopic conductors, revealing how noise behavior transitions from ballistic to diffusive regimes and confirming phase coherence is unnecessary for the characteristic one-third suppression.

Contribution

It introduces a semiclassical approach based on the Boltzmann-Langevin equation to describe shot noise, including effects of impurity scattering, multiple barriers, and inelastic processes.

Findings

Shot noise varies from zero to one-third of Poisson noise across regimes.

The one-third suppression occurs without phase coherence.

Electron heating and inelastic scattering effects are quantified.

Abstract

A semiclassical theory is developed for time-dependent current fluctuations in mesoscopic conductors. The theory is based on the Boltzmann-Langevin equation for a degenerate electron gas. The low-frequency shot-noise power is related to classical transmission probabilities at the Fermi level. For a disordered conductor with impurity scattering, it is shown how the shot noise crosses over from zero in the ballistic regime to one-third of the Poisson noise in the diffusive regime. In a conductor consisting of n tunnel barriers in series, the shot noise approaches one-third of the Poisson noise as n goes to infinity, independent of the transparency of the barriers. The analysis confirms that phase coherence is not required for the occurrence of the one-third suppression of the shot noise. The effects of electron heating and inelastic scattering are calculated, by inserting charge-conserving electron reservoirs between segments of the conductor.