Origin of coherentG-band phonon spectra in single-wall carbon nanotubes

Abstract

Coherent phonons in single wall carbon nanotubes (SWNTs) are observed as oscillations of the differential absorption coefficient as a function of time by means of pump-probe spectroscopy.For the radial breathing mode (RBM) of a SWNT, the coherent phonon signal is understood to be a result of the modulated diameter-dependent energy gaps due to the coherent RBM phonon oscillations. However, this mechanism might not be the dominant contribution to other phonon modes in the SWNT. In particular, for the G band phonons, which correspond to bond-stretching motions, we find that the modulation of the interatomic dipole matrix element gives rise to a strong coherent G band phonon intensity comparable to the coherent RBM phonon intensity. We also further discuss the dependence of coherent G band and RBM phonon amplitudes on the laser excitation pulse width.

Selective coherent phonon-mode generation in single-wall carbon nanotubes

“…In the case of SWNTs, it has been proposed that the driving force from photoexcited carriers interacting with SWNT lattices are displacive, i.e. the shape is close to a step function with a broadening factor determined by the laser pulse width p τ [27]. When we consider the pulse train, we thus expect that the driving force will be like a staircase, where there are some steps originating from the number of pulses N pulse .…”

“…It has been known from earlier studies that coherent phonon oscillations may be driven by a displacive force or impulsive force, where the basic shape of the driving force is close to a step function or delta function, respectively [6,9]. In the case of SWNTs, the driving force from photoexcited carriers interacting with SWNT lattices has been proposed to be displacive, i.e., the shape is close to a step function with a broadening factor determined by the laser pulse width τ p [27]. When we consider the pulse train, we thus expect that the driving force will be like a staircase, where there are some steps originating from the number of pulses N pulse .…”

“…We expect that the origin of this behavior is due to the dependence of the phonon amplitude on the phonon frequency, in which Q m (t) is inversely proportional to m ω upon solving the equation (1), i.e. the higher-frequency phonon modes tend to have a smaller amplitude than the lower-frequency modes [27], as is also indicated by equations (13) and (16). We note that the choice of T T rep G = for the case shown in figure 3 still does not completely give a destructive interference for the RBM.…”