Optical phonon lineshapes and transport in metallic carbon nanotubes under high bias voltage

High bias voltage transport in metallic single-walled carbon nanotubes under axial stress

“…II. The latter model leads to current-voltage characteristic of unstrained SWNTs 5,16 which are in good accordance with experiments. Our one-valley approximation is justified by the fact that the optical frequencies of the zone-center phonons and zoneboundary phonons, and also the electron-phonon coupling in the phononic sectors are rather similar.…”

“…In fact, this was already used by us in Ref. 16 to calculate analytically the current-voltage characteristic of unstrained SWNTs with nonreflecting leads. This is a simplification of the two-valley Boltzmann approach where scattering between the valleys is mediated by zone-boundary and zone-center optical phonons 5,16 which we discussed in Sec.…”

“…The electron-optical phonon interaction in this model leads to an effective inverse scattering time 1/τ ep for the electrons and 2s p /τ ep for the phonons with parameters found in Ref. 16.…”

“…4 The optical phonons decay to lower lying secondary acoustic phonons by phonon-phonon scattering. 16 These then decay to other acoustic phonons or phonons in the substrate and to a smaller amount also in the leads. We show this electron-phonon relaxation path in Fig.…”

“…16 ∂ t n bs/f s c is a phonon-electron scattering term consisting of the interaction with backward or forward scattered electrons. [∂ t n bs/f s ] osc is a thermal phonon relaxation term such that the coupled electronphonon system is not heated up by applying large voltages on the SWNT.…”