Radial Breathing Mode Phonons Research Articles

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

The pulse-train technique within ultrafast pump-probe spectroscopy is theoretically investigated to excite a specific coherent phonon mode while suppressing the other phonon modes generated in single-wall carbon nanotubes (SWNTs). In particular, we focus on the selectivity of the radial breathing mode (RBM) and the G-band for a given SWNT. We find that if the repetition period of the pulse train matches with the integer multiple of the RBM phonon period, the RBM amplitude can be maintained while the amplitudes of the other modes are suppressed. As for the G-band, when we apply a repetition period of a half-integer multiple of the RBM period, the RBM can be suppressed because of destructive interference, while the G-band still survives. It is also possible to keep the G-band and suppress the RBM by applying a repetition period that matches with the integer multiple of the G-band phonon period. However, in this case we have to use a large number of laser pulses having a property of “magic ratio” of the G-band and RBM periods.

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.

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

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.

Raman spectroscopy of optical transitions and vibrational energies of ∼1 nm HgTe extreme nanowires within single walled carbon nanotubes.

This paper presents a resonance Raman spectroscopy study of ∼1 nm diameter HgTe nanowires formed inside single walled carbon nanotubes by melt infiltration. Raman spectra have been measured for ensembles of bundled filled tubes, produced using tubes from two separate sources, for excitation photon energies in the ranges 3.39-2.61 and 1.82-1.26 eV for Raman shifts down to ∼25 cm(-1). We also present HRTEM characterization of the tubes and the results of DFT calculations of the phonon and electronic dispersion relations, and the optical absorption spectrum based upon the observed structure of the HgTe nanowires. All of the evidence supports the hypothesis that the observed Raman features are not attributable to single walled carbon nanotubes, i.e., peaks due to radial breathing mode phonons, but are due to the HgTe nanowires. The observed additional features are due to four distinct phonons, with energies 47, 51, 94, and 115 cm(-1), respectively, plus their overtones and combinations. All of these modes have strong photon energy resonances that maximize at around 1.76 eV energy with respect to incident laser.

Electronic relaxation and coherent phonon dynamics in semiconducting single-walled carbon nanotubes with several chiralities

Coherent phonon (CP) dynamics and electronic relaxation in single-walled carbon nanotubes (SWNTs) are investigated in femtosecond pump-probe experiments. Using a sensitive multichannel lock-in amplifier, chirality-specific electronic relaxation and vibrational dynamics are resolved in SWNT ensembles composed of several chiral systems without the need for selective isolation of the different species by purification. The dynamics of vibrational wave packets are studied based on oscillatory changes in the absorbance of the systems. Modulations corresponding to the radial breathing mode (RBM), observed in the time traces of the absorbance change for the four chiral systems (6,4), (6,5), (7,5), and (8,3), have been analyzed in detail. The vibrational modes of the CP spectra are identified from the two-dimensional distribution of probe photon energy versus Fourier frequency. Resonance conditions and mode frequencies lead to definite chirality assignments. Coherent RBM phonon generation is analyzed using the probe photon energy-dependent amplitude profiles as a result of the spectral shift induced by wave-packet motion on the potential surface. The present study clarifies that the observed probe photon energy dependence is due to both the imaginary and real parts of the third-order susceptibility, corresponding to Raman (and Raman-like) gain and loss processes and to molecular phase modulation, respectively. The imaginary part is the dominant contribution to the modulation in the difference absorbance. It shows probe photon energy dependence in the form of a difference in absorbed photon energy between the spectra that are shifted and unshifted with vibrational frequency. The size of the Huang-Rhys factors from the difference fitting to the (6,4), (6,5), and (8,3) systems are 0.26, 0.32, and 0.75, respectively. The trend of the factors originates in the stiffness differences of the SWNT structures. The real part depends on the derivative of the absorbed photon energy spectrum due to cross-phase modulation, resulting from the change in refractive index during the molecular vibrations. This process induces a probe spectral change, as evidenced by first-derivative fitting using a small number of data points of probe photon energies. The effective nonlinear refractive index for each chiral system is determined to range from 0.2 to $3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm${}^{2}$/W.

Fundamental optical processes in armchair carbon nanotubes

Single-wall carbon nanotubes provide ideal model one-dimensional (1-D) condensed matter systems in which to address fundamental questions in many-body physics, while, at the same time, they are leading candidates for building blocks in nanoscale optoelectronic circuits. Much attention has been recently paid to their optical properties, arising from 1-D excitons and phonons, which have been revealed via photoluminescence, Raman scattering, and ultrafast optical spectroscopy of semiconducting carbon nanotubes. On the other hand, dynamical properties of metallic nanotubes have been poorly explored, although they are expected to provide a novel setting for the study of electron-hole pairs in the presence of degenerate 1-D electrons. In particular, (n,n)-chirality, or armchair, metallic nanotubes are truly gapless with massless carriers, ideally suited for dynamical studies of Tomonaga-Luttinger liquids. Unfortunately, progress towards such studies has been slowed by the inherent problem of nanotube synthesis whereby both semiconducting and metallic nanotubes are produced. Here, we use post-synthesis separation methods based on density gradient ultracentrifugation and DNA-based ion-exchange chromatography to produce aqueous suspensions strongly enriched in armchair nanotubes. Through resonant Raman spectroscopy of the radial breathing mode phonons, we provide macroscopic and unambiguous evidence that density gradient ultracentrifugation can enrich ensemble samples in armchair nanotubes. Furthermore, using conventional, optical absorption spectroscopy in the near-infrared and visible range, we show that interband absorption in armchair nanotubes is strongly excitonic. Lastly, by examining the G-band mode in Raman spectra, we determine that observation of the broad, lower frequency (G(-)) feature is a result of resonance with non-armchair "metallic" nanotubes. These findings regarding the fundamental optical absorption and scattering processes in metallic carbon nanotubes lay the foundation for further spectroscopic studies to probe many-body physical phenomena in one dimension.

Coherent phonons in carbon nanotubes and graphene

We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite specific-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.

Luminescence Properties of Individual Empty and Water-Filled Single-Walled Carbon Nanotubes

The influence of water filling on the photoluminescence (PL) properties of SWCNTs is studied by ensemble and single-molecule PL spectroscopy. Red-shifted PL and PL excitation spectra are observed upon water filling for 16 chiralities and can be used to unambiguously distinguish empty SWCNTs from filled ones. The effect of water filling on the optical transitions is well-reproduced by a continuum dielectric constant model previously developed to describe the influence of the nanotube outer environment. Empty nanotubes display narrower luminescence lines and lower inhomogeneous broadening, signatures of reduced extrinsic perturbations. The radial breathing mode phonon sideband is clearly observed in the PL spectrum of small diameter empty tubes, and a strong exciton-phonon coupling is measured for this vibration. Biexponential PL decays are observed for empty and water-filled tubes, and only the short-living component is influenced by the water filling. This may be attributed to a shortening of the radiative lifetime of the bright state by the inner dielectric environment.

Coherent phonons in excited-state carbon nanotubes: A simulation by tight-binding molecular dynamics

We have made tight-binding molecular dynamics simulations on the coherent phonons induced by electron–phonon coupling in the low energy optically excited states of single-walled carbon nanotubes (SWCNTs) with different diameters and chiralities. It is found that: (1) SWCNT’s radial breathing mode (RBM) and longitudinal optical (LO) mode are easily excited due to their direct coupling with band electrons, which then causes band gap oscillations with the same frequencies as those of RBM and LO modes. (2) Excitation of coherent phonons exhibits an interesting family-behavior. For example, for the family-II tubes, such as (11,0), (17,0) and (10,5) tubes with their mod( n− m,3) =2, the amplitude of their coherent RBM phonons in the first optical E 11 transition is smaller than that in the second optical E 22 one, while the opposite situation appears for a family-I tube with its mod( n−m,3) =1, e.g., (10,0) and (16,0) tubes. (3) Transverse optical (TO) modes cannot be excited in zigzag (10,0) and (11,0) tubes, but can be in a chiral (10,5) tube. The above obtained results are in good agreement with experimental observations.

Phonon sidebands of photoluminescence in single wall carbon nanotubes

The multiphonon-assisted photoluminescence (PL) of the single wall carbon nanotubes (SWNTs) have been studied by solving the Schrödinger equation, showing a set of phonon sidebands, both the Stokes and anti-Stokes lines, which are induced by the longitudinal optical phonon and radial breathing mode phonon. All the calculated results are in a good agreement with the recent experimental PL spectra of the SWNTs [F. Plentz, H. B. Ribeiro, A. Jorio, M. S. Strano, and M. A. Pimenta, Phys. Rev. Lett. 95, 247401 (2005)] and J. Lefebvre and P. Finnie, Phys. Rev. Lett. 98, 167406 (2007)]. In addition, it is very interesting to find in the calculated PL several additional phonon sidebands with rather weak intensities, which are caused by the exciton’s coupling with two kinds of phonons, and expected to be observed in future experiments.

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO2-substrate. By tuning the laser excitation energy across the E33 excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the D mode and the G mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E33 excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G band and D band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E33 resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.

Raman Spectroscopic Evidence for Hot-Phonon Generation in Electrically Biased Carbon Nanotubes

We provide spectroscopic evidence for hot-phonon generation in biased single-walled carbon nanotubes by measuring simultaneously the Stokes and anti-Stokes Raman lines of the G mode and of the radial-breathing mode as a function of current bias. Using Bose-Einstein statistics we can directly calculate the phonon temperature from the intensity ratio of the anti-Stokes to Stokes lines. Upon nanotube biasing we observe (i) an increase of the G mode phonon temperature in contrast to the radial-breathing mode phonons that remain thermalized at room temperature, and (ii) no softening of the G mode. Based on these observations, we exclude current-induced thermal heating of the nanotube.

Nonequilibrium Green's Function Treatment of Phonon Scattering in Carbon-Nanotube Transistors

We present the detailed treatment of dissipative quantum transport in carbon nanotube field-effect transistors (CNTFETs) using the non-equilibrium Green's function formalism. The effect of phonon scattering on the device characteristics of CNTFETs is explored using extensive numerical simulation. Both intra-valley and inter-valley scattering mediated by acoustic (AP), optical (OP), and radial breathing mode (RBM) phonons are treated. Realistic phonon dispersion calculations are performed using force-constant methods, and electron-phonon coupling is determined through microscopic theory. Specific simulation results are presented for (16,0), (19,0), and (22,0) zigzag CNTFETs that are in the experimentally useful diameter range. We find that the effect of phonon scattering on device performance has a distinct bias dependence. Up to moderate gate biases the influence of high-energy OP scattering is suppressed, and the device current is reduced due to elastic back-scattering by AP and low-energy RBM phonons. At large gate biases the current degradation is mainly due to high-energy OP scattering. The influence of both AP and high-energy OP scattering is reduced for larger diameter tubes. The effect of RBM mode, however, is nearly independent of the diameter for the tubes studied here.

Electron transport in semiconducting chiral carbon nanotubes

The authors report on electron transport characteristics for semiconducting, single wall, chiral carbon nanotubes. The Boltzmann transport equation is solved indirectly by the ensemble Monte Carlo method. The basis for the transport calculations is provided by electronic structure calculations in the framework of a simple tight binding model. Scattering mechanisms considered are due to the electron-phonon interactions involving longitudinal acoustic, longitudinal optic, and radial breathing mode phonons. Due to the smaller Brillouin zone, Umklapp scattering processes occur with much greater frequency in chiral carbon nanotubes than in achiral nanotubes. The transient and steady-state transport characteristics are found to be dependent on the chirality for semiconducting carbon nanotubes with similar diameters.

Low- and high-field transport studies for semiconducting carbon nanotubes

We calculate low- and high-field electron transport characteristics for semiconducting, single-wall, zigzag carbon nanotubes with diameters ranging from small to relatively large. The Boltzmann transport equation is solved directly using an iterative technique and indirectly by the ensemble Monte Carlo method. The basis for the transport calculation is provided by electronic structure calculations within the framework of a simple tight-binding model. Scattering mechanisms considered are due to the electron–phonon interactions involving longitudinal acoustic, longitudinal optic, and radial breathing-mode phonons. Results show significant effects of tube diameter on both low- and high-field transport characteristics.

Electron Transport in Semiconducting Chiral Carbon Nanotubes

AbstractWe report on electron transport characteristics for semiconducting, single wall, chiral carbon nanotubes. The Boltzmann transport equation is solved indirectly by the Ensemble Monte Carlo method. The basis for the transport calculations is provided by electronic structure calculations within the framework of a simple tight binding model. Scattering mechanisms considered are due to the electron-phonon interactions involving longitudinal acoustic, longitudinal optic, and radial breathing mode phonons. Results show significantly increased Umklapp scattering processes due to the reduced Brillouin zone compared to zigzag nanotubes. This results in increased transient velocity oscillation and negative differential mobility.

Effects of radial breathing mode phonons on charge transport in semiconducting zigzag carbon nanotubes

We report ensemble Monte Carlo transport simulation results for single-wall semiconducting zigzag carbon nanotubes. The effects of electron scattering by radial breathing mode phonons are investigated. The basis for the Monte Carlo simulations is provided by electronic structure calculations in the framework of the tight-binding model. Scattering mechanisms considered are due to electron-phonon interactions involving longitudinal acoustic, longitudinal optical, and radial breathing mode phonons. The steady-state velocity is lower for low and moderate electric fields when radial breathing mode phonons are taken into account. Electron scattering by radial breathing mode phonons does not appear to affect strongly the steady-state electron transport within a carbon nanotube at high electric fields. Oscillations in the transient velocity show increased damping.