Decay of a plasmon into neutral modes in a carbon nanotube

TL;DR

This paper analyzes how plasmons decay into neutral modes in a disorder-free carbon nanotube, revealing temperature-dependent power-law behaviors and universal crossover functions influenced by doping and electron interactions.

Contribution

It provides a detailed theoretical analysis of plasmon decay mechanisms into neutral modes in carbon nanotubes, including the effects of doping and finite-length geometries.

Findings

Decay rates follow power-laws with temperature at zero doping.

Universal crossover functions describe decay rates at finite doping.

Decay mechanisms involve phonon-assisted and Umklapp backscattering.

Abstract

We evaluate the rate of energy loss of a plasmon in a disorder-free carbon nanotube. The plasmon decays into neutral bosonic excitations of the electron liquid. The process is mediated either by phonon-assisted backscattering of a single electron, or Umklapp backscattering of two electrons. To lowest order in the backscattering interactions the partial decay rates are additive. At zero doping the corresponding decay rates scale as power-laws of the temperature with positive and negative exponents for the two mechanisms, respectively. The precise values of the exponents depend on the Luttinger liquid parameter. At finite doping the decay rates are described by universal crossover functions of frequency and chemical potential measured in units of temperature. In the evaluation of the plasmon decay, we concentrate on a finite-length geometry allowing excitation of plasma resonances.