Phonon-Induced Current Noise in Single-Walled Carbon Nanotubes across the Ballistic-Diffusive Crossover

TL;DR

This paper theoretically investigates how phonon-induced current noise in single-walled carbon nanotubes varies with system length, revealing a maximum at the mean free path and different scaling behaviors in ballistic and diffusive regimes.

Contribution

It provides a detailed theoretical analysis of the length dependence of phonon-induced current noise across ballistic and diffusive regimes, incorporating complex scattering processes.

Findings

Maximum noise occurs when system length is comparable to electron mean free path.

In ballistic regime, noise scales linearly with length.

In diffusive regime, noise decays as a power law with exponent 3.81.

Abstract

We theoretically elucidate the system length ($L$) dependence of phonon-induced current noise in carbon nanotubes at room temperature over a broad range, encompassing the quantum ballistic and classical diffusive regimes. The power spectral density for the current noise is maximally enhanced when $L$ is comparable to the mean free path $L_0$ of an electron. In the ballistic limit of $L/L_0\ll 1$, the power spectral density increases in proportion to $L$, whereas in the diffusive limit of $L/L_0\gg 1$, it shows a power-law decay $L^{-\alpha}$ with a scaling parameter $\alpha=3.81$. The noise decay for single-walled carbon nanotubes is faster than that previously predicted based on a simple model because of the various electron-phonon scattering processes and the complex energy dependence of the phonon relaxation time.