Decay of a plasmon into neutral modes in a carbon nanotube

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.

10 pages, 4 figures

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• Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes
• Thermal radiation as a probe of one-dimensional electron liquids
• Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquids
• Quantum criticality in a Mott pn-junction in an armchair carbon nanotube