Polarization dependence of coherent phonon generation and detection in highly-aligned single-walled carbon nanotubes

Abstract

We have investigated the polarization dependence of the generation and detection of radial breathing mode (RBM) coherent phonons (CP) in highly-aligned single-walled carbon nanotubes. Using polarization-dependent pump-probe differential-transmission spectroscopy, we measured RBM CPs as a function of angle for two different geometries. In Type I geometry, the pump and probe polarizations were fixed, and the sample orientation was rotated, whereas, in Type II geometry, the probe polarization and sample orientation were fixed, and the pump polarization was rotated. In both geometries, we observed an almost complete quenching of the RBM CPs when the pump polarization was perpendicular to the nanotubes. For both Type I and II geometries, we have developed a microscopic theoretical model to simulate CP generation and detection as a function of polarization angle and found that the CP signal decreases as the angle goes from 0• (parallel to the tube) to 90• (perpendicular to the tube). We compare theory with experiment in detail for RBM CPs created by pumping at the E44 optical transition in an ensemble of single-walled carbon nanotubes with a diameter distribution centered around 3 nm, taking into account realistic band structure and imperfect nanotube alignment in the sample. We theoretically determined a cos 8 (θ) dependence for Type I CP spectroscopy experiments and a cos 4 (φ) polarization dependence for Type II CP spectroscopy experiments, and after including misalignment effects to our fitting, we determined the nematic order parameter of our sample to be 0.81.

Theory of coherent phonons in carbon nanotubes and graphene nanoribbons

“…The lowest frequency coherent phonons that can be photoexcited in SWNTs using ultrafast laser pulses are coherent RBM phonons with phonon wavevector q = 0 corresponding to a mode in which the diameter of the nanotube periodically expands and contracts. These coherent RBM phonons have been studied experimentally by several groups [51][52][53][54][55][56]. In addition to the lower frequency coherent RBM modes, higher frequency q = 0 coherent G mode phonons have also been observed [57,58].…”

“…A more elaborate study of polarization dependence of coherent phonons in samples where the tubes are highly aligned was undertaken by Booshehri et al [56]. These authors used polarization-dependent differential-transmission pump-probe CP spectroscopy to investigate the polarization dependence of coherent RBM phonons in highly aligned single-walled carbon nanotube thin films transferred onto a sapphire substrate with a diameter distributed between 1 and 5 nm centered around 3 nm [124].…”

“…Within each family, CP intensity tends to decrease as the chiral angle and tends to increase as we go from Family 22 to Family 25. The top panel of figure 21 shows the corresponding [56]. In (a) the pump and probe polarizations are fixed and the sample is rotated through an angle θ.…”

“…Using those simulated results, they found a cos 8 (θ ) dependence in geometry I CP spectra and a cos 4 (φ) polarization dependence in geometry II CP spectra. In fitting experiment to theory, misalignment effects were taken into account, and it was determined that data from both geometry I and II experiments could be fit assuming the nematic order [56]). …”

Coherent phonons in carbon based nanostructures

“…The theory and modeling of coherent phonons in carbon nanotubes, carbon nanoribbons, and graphene has been discussed before in several different papers, 12,13,[15][16][17][18][19] including two recent review articles. 20,21 The details of the calculations are discussed there and here we just provide an overview.…”