Using pre-designed 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 radial breathing mode oscillations.PACS numbers: 78.67. Ch,71.35.Ji, Single-walled carbon nanotubes (SWNTs), hollow onedimensional nanostructures with unique electronic, mechanical, and optical properties, come in a variety of species, or chiralities. Some of them are metallic and others semiconducting, depending on their chiral indices (n,m) [1,2,3]. This diversity, while making them such unusual nanomaterials, often makes it challenging to extract reliable parameters on chirality-dependent properties from experimental results on ensemble samples. Currently, there are world-wide efforts on SWNT purification, separation, and enrichment, producing promising results [4,5,6,7,8]. However, a standard for fabrication of these samples has yet to be established.Here, we present a novel method that allows us to study single-chirality nanotubes even though the sample contains nanotubes of many different chiralities. Specifically, we have utilized the techniques of femtosecond pulse shaping [9,10,11] in ultrafast pump-probe spectroscopy of SWNTs to selectively excite the coherent lattice vibrations [12,13] of the radial breathing mode (RBM) of specific chiralities. The excitation spectra of such coherent phonons (CPs) provide chirality-specific information on the processes of light absorption, phonon generation, and phonon-induced band structure modulations in unprecedented detail. In particular, the excitation-energy-dependence of the phase of the CP oscillations provides direct, time-domain evidence that band gap oscillations follow the diameter oscillations in the RBM coherent phonon mode.The sample studied was a micelle-suspended SWNT solution, where the SWNTs (HiPco batch HPR 104) were suspended as individuals with sodium cholate [14]. The optical setup was that of standard degenerate pumpprobe spectroscopy, but chirality selectivity was achieved by using multiple pulse trains, with a pulse-to-pulse interval corresponding to the period of a specific RBM mode. Among different species of nanotubes, those having RBM frequencies that are matched to the repetition rate of multiple pulse trains will generate large amplitude coherent oscillations with increasing oscillatory response to each pulse, while others will have diminished coherent responses [15,16,17]. The tailoring of multiple pulse trains from femtosecond pulses was achieved using the pulse-shaping technique described elsewhere [10]. Pulse trains are incident on an ensemble of nanotubes as a pump beam, and coherent RBM osc...

The definition of the coherent phonon amplitude in Eq. ͑54͒ of our paper contains a minor misprint and should read D q ͑ t ͒ϵ͗ b q ͑ t ͒ϩb Ϫq † ͑ t ͒ ͘. ͑54͒ We would like to point out that the matrix element in Eq. ͑49͒ underestimates the piezoelectric electron-phonon interaction by a factor of 4 and should readThis same factor of 4 also appears in the driving function expressions in Eqs. ͑81͒, ͑85͒, and ͑86͒ which now read ͑86͒As a result, Figs. 10-17 in our paper need to be changed and the revised figures are shown below. The paragraph on page 235316-14 describing the results of Fig. 12 needs to be replaced by the following.''In our simulation, we find that piezoelectric and deformation potential contributions to the driving function are comparable. This is seen in Fig. 12 where S piezo (z) and S def (z), along with their sum, are plotted at tϭ2 ps. In this example, we find that S piezo (z) makes the dominant contribution to S(z,t) as can be seen in Fig. 12.'' FIG. 10. Driving function, S(z,t), for the coherent LA phonon wave equation as a function of position and time for the In x Ga 1Ϫx N diode structure and laser pumping parameters in Table II. S(z,t) is computed using the full microscopic expression of Eq. ͑79͒. FIG. 11. Driving function, S(z,t), in the simplified loaded string model for the coherent LA phonon wave equation as a function of position and time for the In x Ga 1Ϫx N diode structure and laser pumping parameters in Table II. FIG. 12. Driving function, S(z,t), in the simplified loaded string model at tϭ2 ps for the coherent LA phonon wave equation as a function of position for the In x Ga 1Ϫx N diode structure and laser pumping parameters in Table II. The total driving function, S(z,t), is the sum of piezoelectric and deformation potential contributions, S piezo (z,t) and S def (z,t).PHYSICAL REVIEW B 66, 079903͑E͒ ͑2002͒

We have developed a microscopic theory for the generation and detection of coherent phonons in armchair and zigzag graphene nanoribbons using an extended tight-binding model for the electronic states and a valence force field model for the phonons. The coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We examine the coherent phonon radial breathing like mode amplitudes as a function of excitation energies and nanoribbon types. For photoexcitation near the optical absorption edge the coherent phonon driving term for the radial breathing like mode is much larger for zigzag nanoribbons where transitions between localized edge states provide the dominant contribution to the coherent phonon driving term. Using an effective mass theory, we explain how the armchair nanoribbon width changes in response to laser excitation.

We have carried out an ultrahigh-field cyclotron resonance study of n-type In 1Ϫx Mn x As films, with Mn composition x ranging from 0% to 12%, grown on GaAs by low-temperature molecular-beam epitaxy. We observe that the electron cyclotron resonance peak shifts to lower field with increasing x. A detailed comparison of experimental results with calculations based on a modified Pidgeon-Brown model allows us to estimate the s-d and p-d exchange-coupling constants, ␣ and ␤, for this important III-V dilute magnetic semiconductor system.

Using a macroscopic ensemble of highly-enriched (6,5) single-wall carbon nanotubes, combined with high signal-to-noise ratio, time-dependent differential transmission spectroscopy, we have generated vibrational modes in an ultrawide spectral range (10-3000 cm −1 ). A total of fourteen modes were clearly resolved and identified, including fundamental modes of A, E1, and E2 symmetries and their combinational modes involving two and three phonons. Through comparison with CW Raman spectra as well as calculations based on an extended tight-binding model, we were able to identify all the observed peaks and determine the frequencies of the individual and combined modes. We provide a full summary of phonon frequencies for (6,5) nanotubes that can serve as a basic reference with which to refine our understanding of nanotube phonon spectra as well as a testbed for new theoretical models.