Acoustic Phonon Growth Rate In Undoped Graphene Due To External Temperature Gradient

Phonon generation/amplification in nanostructures is of primary importance for engineering device applications such as Phonon laser, phonon spectrometer, ultrafast optical modulators and other device based on acousto-electro/magneto/thermo effects. In this paper we report our theoretical calculation of acoustic phonon growth rate in single layer graphene in presence of external temperature gradient within the framework of Boltzmann transport equation under the linear response regime in the short wavelength limit, ql >> 1. Using this formalism we produce analytical result for attenuation/amplification coefficient for acoustic phonons and from there obtain the threshold value of temperature gradient for the occurrence of amplification of acoustic phonons in single layer graphene.