Phonons In Single-walled Carbon Nanotubes Research Articles

Asymmetry in Raman Resonant Excitation Profiles of Single-Wall Carbon Nanotubes: The Role of Kohn Anomaly, Optical Transition Order, and State-Mixing

Examination of Raman resonant excitation profiles (REPs) of the radial breathing mode (RBM) and G-band phonons has provided new insights into the coupling between excitons and phonons in single-wall carbon nanotubes (SWCNTs). For example, measurements of REPs of the longitudinal optical (LO) and transverse optical (TO) G-band phonons of highly pure, single semiconducting species SWCNT samples displayed a high degree of asymmetry when comparing the Raman intensity at the incident and scattered Raman resonances for excitation via E22 S. The LO and TO phonon REP asymmetries were explained using a molecular picture as due to a self-interference between Condon and non-Condon terms in the Raman polarizability, due to a vibrational coordinate dependence in transition dipole moment. This results in the observation that the Raman intensity at the scattered resonance is always lower in intensity than that of the incident resonance, a consequence of the failure of the Franck-Condon approximation. This is contrary to the symmetrical G-band REP expected by conventional theory and observed for RBM REPs. More recently, these Raman REP studies were expanded to include metallic armchair species, (5,5) through (8,8), excited via E11 M. Similar asymmetries to those of semiconducting SWCNTs were observed in the TO phonons of these armchair species while no asymmetry was observed for their respective RBM REPs, emphasizing the similarity in the excitonic nature of the optical states of these two electronic types of SWCNTs. In addition, a new model was developed in terms of a condensed matter formalism involving phonon-mediated state-mixing of dark and bright excitonic states to successfully explain the asymmetry in G-band phonon REPs of both semiconductor and armchair SWCNT species. Here, we extend our understanding of this optical phenomenon by considering the roles that Kohn anomaly, optical transition order and phonon-mediated state-mixing play in the degree of asymmetry observed for SWCNT phonon REPs. To examine the effect of the Kohn anomaly, we measured G-band phonon REPs of another electronic type of SWCNT, known as narrow-gap semiconductors (NGS), such as the (7,4) and (10,4) species, whose electronic band structure is similar to that of metallic armchair SWCNTs with the exception of a small band gap on the order of 10 meV. Of special interest in NGS SWCNT structures are the LO phonons, which are strongly frequency-softened and broadened through the Kohn anomaly due to strong coupling of LO phonons with the two Fermi points. Such a strong interaction should further enhance the observed REP asymmetry due to non-Condon-based self-interference. Furthermore, NGS-type SWCNT species, such as the (7,4) and (10,4), possess the additional trigonal warping splitting term in their band structure, which causes each optical transition to split into two, allowing for potential quantum interference between upper and lower branch transitions which may produce further asymmetry. To examine the role of optical transition order on REP asymmetry, we measured RBM and G-band REPs for multiple semiconducting chiralities such as (8,3), (9,1), (5,4), (7,6), (9,4), and (8,6) across multiple optical transitions ranging from E11 S-E44 S. Generally, the degree of asymmetry increased with increasing transition order for the same SWCNT species for the LO phonon. Additionally, we reexamined whether asymmetry exists in RBM REPs of semiconducting species excited via E11 S, where the RBM phonon energy is greater than or equal to the electronic linewidth of the transition, allowing resolution of both incident and scattered resonances of the REP. This was not possible in previous measurements because the electronic linewidths of the optical transitions involved were greater than the RBM phonon energies. Finally, to test the validity of the phonon-mediated state-mixing model, we prepared isotopically pure 12C- and 13C-samples of single chiralities (7,5), (7,6), and (7,7). Using these samples, excited via E22 S for (7,5) and (7,6) and via E11 M for (7,7), we compared the measured G-band phonon REPs for both isotopes of the same chirality. While 13C-SWCNTs look identical to their 12C-counterparts in terms of electronic band structure and optical transition energies, the phonons in their Raman spectra decrease in frequency by a factor of √(12/13) due to the isotope effect. If G-band phonon REP asymmetry is really due to mixing of dark and bright excitonic states, mediated by G-band or K-point phonons, which in turn causes quantum interference between excitonic states or transfer of oscillator strength from one excitonic state to another, then a change in the phonon energy mediating such an interaction should cause a visible change in the degree of asymmetry of the REP for the same chirality. The change in the degree of REP asymmetry provides a measure of the magnitude of state-mixing.

Engineering Intrinsic and Extrinsic Quantum Interference in Electronic States of Carbon Nanotubes Measured By Resonant Raman Scattering

Examination of Raman resonant excitation profiles (REPs) of the radial breathing mode (RBM) and G-band phonons has provided a wealth of new insights into the coupling between electrons/excitons and phonons in single-wall carbon nanotubes. Very recently, new measurements of the REPs of the G-band phonon on highly pure, single semiconducting species SWCNT samples displayed a high degree of asymmetry when comparing the Raman intensity at the incident and scattered Raman resonances for either the first or second optical transitions. The REP asymmetry is due to a self-interference between Condon and non-Condon terms in Raman polarizability, where the effect of the non-Condon term becomes visible in the weak exciton-phonon coupling regime. This results in the observation that the Raman intensity at the scattered resonance is always lower in intensity than that of the incident resonance, a consequence of the failure of the Franck-Condon approximation. This is contrary to the symmetrical G-band REP expected by theory and observed for RBM REPs. At even higher energy optical transitions, quantum interference can occur between a pair of closely spaced electronic transitions, such as the third and fourth transitions in certain semiconducting species, where the scattered resonance of the lower energy optical transition interferes constructively or destructively with the incident resonance of the higher energy optical transition. This is on top of the already underlying self-interference effects stemming from the non-Condon contribution, creating a highly complex and rich energy structure for SWCNT Raman measurements of high energy phonon modes.Here, we examine the origin of these deviations from the expected symmetrical REPs for exciton-mediated, one-phonon Raman processes in SWCNTs, by expanding the previous measurements on the RBM and G-band phonons to include additional pure SWCNT species as a function of chiral angle, diameter, and electronic type. We measured the intrinsic non-Condon-induced self-interference of the G-band in the “metallic” family of SWCNTs, consisting of the so-called armchair and narrow-gap semiconductor (NGS)-type nanotube species. Specifically, we examined the diameter dependence of REP asymmetry of armchairs ranging from (5,5) to (8,8), as well as the NGS-species (7,4). The addition of these particular nanotube structures allows the examination of the effect of electronic type on REP behavior, where the unique linear band structure of armchair and quasi-linear band structure of NGS species produces additional electron-phonon coupling resonances through the so-called Kohn anomaly, further enhancing the observed REP asymmetry due to non-Condon-based self-interference. Preliminary data already suggests that armchair species exhibit the largest degree of G-band REP asymmetry relative to other species. Furthermore, NGS-type SWCNT species, such as the (7,4), possess the additional trigonal warping splitting term in their band structure, which causes each optical transition to split into two, allowing for additional quantum interference between upper and lower branch transitions.To further explore and control the degree of quantum interference between transitions possible, we applied mechanical uniaxial strain to single-chirality SWCNTs embedded in stretchable polymer films to further induce and enhance quantum interference for chiralities such as the (12,4), (8,6) and (7,4) and measured their RBM and G-band REPs as a function of strain. Theoretical calculations predict that the application of a few percent uniaxial strain will cause the third and fourth optical transitions in certain type-I semiconductor species and the trigonal-warping split transitions in NGS-type tubes to move toward one another in energy, thereby inducing quantum interference. In this situation, interference can be manipulated and, in some cases where quantum interference did not previously exist, created artificially, allowing a broader range of REP asymmetries to be examined.

Measurements of the Population Lifetime of D Band and G′ Band Phonons in Single-Walled Carbon Nanotubes

We report time-resolved incoherent anti-Stokes Raman scattering measurements of the dynamics of the D and G' bands in single-walled carbon nanotubes at excitation energies of 1.51 and 1.63 eV over the temperature range 4-330 K. The measurements indicate that the population lifetimes (~1 ps) of the phonons responsible for the D band are dependent on nanotube type. The temperature dependencies are consistent with anharmonic decay of the phonons into one low (<190 cm(-1)) and one high energy phonon.

Dephasing ofG-band phonons in single-wall carbon nanotubes probed via impulsive stimulated Raman scattering

We have studied the coherent dynamics of G-band phonons in single-walled carbon nanotubes through impulsive stimulated Stokes and anti-Stokes Raman scattering. The probe energy dependence of phonon amplitude as well as preferential occurrence between Stokes and anti-Stokes components in response to chirped-pulse excitation are well explained within our model. The temperature dependence of the observed dephasing rate clearly exhibits a thermally-activated component, with an activation energy that coincides with the frequency of the radial breathing mode (RBM). This fact provides a clear picture for the dephasing of optical phonons by random frequency modulation via interaction with the RBM through anharmonicity.

Chirality dependence of coherent phonon amplitudes in single-wall carbon nanotubes

We simulate the ultrafast dynamics of laser-induced coherent phonons in single-wall carbon nanotubes (SWNTs). In particular, we examine the coherent phonon amplitude of the radial breathing mode (RBM) as a function of excitation energy and chirality. We find that the RBM coherent phonon amplitudes are very sensitive to changes in excitation energy and are strongly chirality dependent. We discuss how the SWNT diameter changes in response to femtosecond laser excitation and under what conditions the diameter of a given SWNT will initially increase or decrease. An effective-mass theory for the electron-phonon interaction gives a physical explanation for these phenomena.

Curvature-induced Symmetry Lowering and Anomalous Dispersion of Phonons in Single-Walled Carbon Nanotubes

ABSTRACTHere we report rich and new resonant Raman spectral features for several sub-nanometer diameter single wall carbon nanotubes (sub-nm SWNTs) samples grown using chemical vapor deposition technique operating at different temperatures. We find that the high curvature in sub-nm SWNTs leads to (i) an unusual S-like dispersion of the G‑band frequency due to perturbations caused by the strong electron-phonon coupling, and (ii) an activation of diameter-selective intermediate frequency modes that are as intense as the radial breathing modes (RBMs). Furthermore, an analytical approach which includes the effects of curvature into the overlap integral and the energy gap between the van Hove singularities is discussed. Lastly, we show that the phonon spectra for sub-nm SWNTs obtained from the molecular dynamic simulations which employs a curvature-dependent force field concur with our experimental observations.

Hydrostatic-pressure induced phase transition of phonons in single-walled nanotubes

We study the effect of the hydrostatic pressure on the phonons in single-walled carbon nanotubes (SWNTs) in a magnetic field. We calculate the magnetic moments of the phonons using a functional integral technique, and find that the phonons in SWNTs undergo a pressure-induced phase transition from the paramagnetic phase to the diamagnetic phase under hydrostatic pressure 2 GPa. We explain the mechanism of generating this phase transition.

Resonant coherent phonon spectroscopy of single-walled carbon nanotubes

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.

Electron and phonon renormalization near charged defects in carbon nanotubes

Owing to their influence on electrons and phonons, defects can significantly alter electrical conductance, and optical, mechanical and thermal properties of a material. Thus, understanding and control of defects, including dopants in low-dimensional systems, hold great promise for engineered materials and nanoscale devices. Here, we characterize experimentally the effects of a single defect on electrons and phonons in single-wall carbon nanotubes. The effects demonstrated here are unusual in that they are not caused by defect-induced symmetry breaking. Electrons and phonons are strongly coupled in sp(2) carbon systems, and a defect causes renormalization of electron and phonon energies. We find that near a negatively charged defect, the electron velocity is increased, which in turn influences lattice vibrations locally. Combining measurements on nanotube ensembles and on single nanotubes, we capture the relation between atomic response and the readily accessible macroscopic behaviour.

Direct Measurement of the Lifetime of Optical Phonons in Single-Walled Carbon Nanotubes

Time-resolved anti-Stokes Raman spectroscopy has been applied to probe the dynamics of optical phonons created in single-walled carbon nanotubes by femtosecond laser excitation. From measurement of the decay of the anti-Stokes Raman signal in semiconducting nanotubes of (6,5) chiral index, a room-temperature lifetime for G-mode phonons of 1.1+/-0.2 ps has been determined. This lifetime, which reflects the anharmonic coupling of the G-mode phonons to lower-frequency phonons, is important in assessing the role of nonequilibrium phonon populations in high-field transport phenomena.

Infrared active phonons in single-walled carbon nanotubes

We present IR reflectance spectra of samples containing single-walled carbon nanotubes and compare them with measurements made on graphite. Weak structures near the graphite modes but shifted towards higher frequencies were found. We assign these structures to IR-active phonons of single-walled nanotubes. Our experimental results suggest that while roughly in agreement with the experiment, further and more accurate calculations of the phonon frequencies of single-walled carbon nanotubes are necessary.