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Register a new userResonant Coherent Phonon Spectroscopy of Single-Walled Carbon Nanotubes
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Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one can generate and detect coherent phonons in chirality-specific semiconducting single-walled carbon nanotubes. The signals are resonantly enhanced when the pump photon energy coincides with an interband exciton resonance, and analysis of such data provides a wealth of information on the chirality-dependence of light absorption, phonon generation, and phonon-induced band structure modulations. To explain our experimental results, we have developed a microscopic theory for the generation and detection of coherent phonons in single-walled carbon nanotubes using a tight-binding model for the electronic states and a valence force field model for the phonons. We find that the coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We compared our theoretical results with experimental results on mod 2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod 2 families. We also find that the coherent phonon intensities are considerably weaker in mod 1 nanotubes in comparison with mod~2 nanotubes, which is also in excellent agreement with experiment.
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We have observed large-amplitude coherent phonon oscillations of radial breathing modes (RBMs) in single-walled carbon nanotubes excited through the lowest-energy (E11) interband transitions. In contrast to the previously-studied coherent phonons excited through higher-energy (E22) transitions, these RBMs show comparable intensities between (n-m) mod 3 = 1 and -1 nanotubes. We also find novel non-resonantly excited RBMs over an excitation range of ~300 meV above the E11 transition, which we attribute to multi-phonon replicas arising from strong exciton-phonon coupling.
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 a very nearly 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 degrees (parallel to the tube) to 90 degrees (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 present results of wavelength-dependent ultrafast pump-probe experiments on micelle-suspended single-walled carbon nanotubes. The linear absorption and photoluminescence spectra of the samples show a number of chirality-dependent peaks, and consequently, the pump-probe results sensitively depend on the wavelength. In the wavelength range corresponding to the second van Hove singularities (VHSs), we observe sub-picosecond decays, as has been seen in previous pump-probe studies. We ascribe these ultrafast decays to intraband carrier relaxation. On the other hand, in the wavelength range corresponding to the first VHSs, we observe two distinct regimes in ultrafast carrier relaxation: fast (0.3-1.2 ps) and slow (5-20 ps). The slow component, which has not been observed previously, is resonantly enhanced whenever the pump photon energy resonates with an interband absorption peak, and we attribute it to radiative carrier recombination. Finally, the slow component is dependent on the pH of the solution, which suggests an important role played by H$^+$ ions surrounding the nanotubes.
High-field magneto-optical spectroscopy was conducted on highly-selected chiral (6,5) specific single-walled carbon nanotubes. Spectra of phonon sidebands in both 1st and 2nd sub-bands were observed to be unchanged by the application of an external magnetic field up to 52 T. Our analyses led to the conclusion that both phonon sidebands in respective sub-band originate from the dark K-momentum singlet (D-K-S) excitons. Moreover, while the relative ordering between the bandedge bright exciton and its zero-momentum anti-bonding counterpart was found to be opposite for the 1st and 2nd sub-bands, the relative ordering between the D-K-S exciton and the band-edge bright exciton was clarified to be the same for both sub-bands. Energy of these D-K-S excitons was estimated to be ~ 21.5 and ~ 37.3 meV above the band-edge bright exciton for the 1st and 2nd sub-bands, respectively.
The radial-breathing-like phonon modes (RBLMs) of the double-walled carbon nanotubes are studied in a simple analytical model, in which the interaction force constants (FCs) can be obtained analytically from the continuous model. The RBLMs frequencies are obtained by solving the dynamical matrix, and their relationship with the tube radii can be obtained analytically, offering a powerful experimental tool for determining precisely the radii of the multi-walled carbon nanotubes.
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