Shot noise in long conductors

TL;DR

This paper demonstrates that in long conductors, finite-frequency shot noise can reach the full shot noise level depending on the sample length and frequency, with implications for experimental measurements.

Contribution

It introduces a theoretical analysis using the drift-diffusion-Langevin equation to determine shot noise behavior in long conductors at various frequencies.

Findings

Shot noise approaches full shot noise level in long conductors at certain frequencies.

The critical length for shot noise significance depends on frequency and material parameters.

High-frequency shot noise can be large regardless of sample length.

Abstract

Using the 'drift-diffusion-Langevin' equation we show that, at least in one geometry, finite-frequency shot noise is of the order of the 'full' shot noise $2eI$ provided the sample is either short or long enough, $L > L_0(\omega)$. Here $L_0(\omega) = D'/\lph \omega$ with $D'$ the effective diffusion coefficient, $\lph$ the electron-phonon energy relaxation length with energy transfer $eV$, and $\omega$ the observation frequency. For example, in a typical 'zero frequency' experiment, actually performed at 10 KHz, shot noise may be large for $L$ larger than a few centimeters. At 100 MHz shot noise may be large for any length of the sample. The physical reason for this result -- a competition between the equilibration length and the dynamic screening length -- is discussed in the text.