Chirality-Selective Excitation of Coherent Phonons in Carbon Nanotubes by Femtosecond Optical Pulses

Using predesigned trains of femtosecond optical pulses, we have selectively excited coherent phonons of the radial breathing mode of specific-chirality single-walled carbon nanotubes within an ensemble sample. By analyzing the initial phase of the phonon oscillations, we prove that the tube diameter initially increases in response to ultrafast photoexcitation. Furthermore, from excitation profiles, we demonstrate that an excitonic absorption peak of carbon nanotubes periodically oscillates as a function of time when the tube diameter undergoes coherent radial breathing mode oscillations.

Figure 1

(a) (Left) Time-domain transmission modulations due to coherent RBM vibrations in an ensemble SWNT solution generated using standard pump-probe techniques without pulse shaping; (Right) Fourier transformation of time-domain oscillations with chirality assigned peaks. (b–f) (Left) Time-domain coherent RBM oscillations selectively excited by multiple pulse trains via pulse shaping with corresponding repetition rates of $7.07-6.15\mathrm{THz}$; (Right) Fourier transformations of corresponding oscillations, with their dominant nanotube chirality ($n$, $m$) indicated. In (f), the pump repetition rate was intentionally tuned to the middle of the RBM frequencies for (11, 3) and (10, 5) nanotubes.

Figure 2

(a) Differential transmission as a function of time delay at probe wavelengths of 780 nm, 795 nm, and 810 nm for the selective RBM excitation of the (11, 3) nanotubes. There is a $\pi$ phase shift between the 780 nm and 810 nm data. These three wavelengths correspond to below, at, and above the second exciton resonance, respectively, of (11, 3) nanotubes. (b,c) Differential transmission as a function of time delay together with the pump pulse train as well as fit to exponentially-decaying sinusoidal oscillations.

Figure 3

Coherent phonon intensity at the RBM frequency as a function of pump-probe energy for several mod 2 semiconducting nanotubes at the $E_{22}$ transition. Right: experimental spectra; left: simulated spectra. The upper four curves in each panel are for nanotubes in Family 22 and the lower four curves are for tubes in Family 25. Each curve is labeled with the chirality ($n$, $m$) and the RBM phonon energy in meV and offset for clarity.

Figure 4

Excitation profile of coherent phonons as evidence of band gap modulations. (a) Phonon amplitude as a function of probe energy fit to the derivative of a Lorentzian peak. (b) Lorentzian reconstructed from (a). (c) Photoluminescence (PL) excitation profile for (11, 3) tubes.