We present a systematic study of the Raman spectra of optical phonons in graphene monolayers under tunable uniaxial tensile stress. Both the G and 2D bands exhibit significant red shifts. The G band splits into 2 distinct subbands (G ؉ , G ؊ ) because of the strain-induced symmetry breaking. Raman scattering from the G ؉ and G ؊ bands shows a distinctive polarization dependence that reflects the angle between the axis of the stress and the underlying graphene crystal axes. Polarized Raman spectroscopy therefore constitutes a purely optical method for the determination of the crystallographic orientation of graphene.S ince the discovery of mechanical cleavage of graphene from graphite crystals (1), graphene has attracted intense interest because of properties that include high electron mobility (2, 3), novel quantum Hall physics (4, 5), superior thermal conductivity (6), and unusually high mechanical strength (7). Raman spectroscopy has emerged as a key diagnostic tool to identify single-layer graphene sheets (8) and probe their physical properties (9, 10). Because strain induces shifts in the vibrational frequencies, Raman spectroscopy can be applied to map built-in strain fields during synthesis (11) and device fabrication, as well as measure load transfer in composites. The rate of shift of the phonon frequencies with strain depends on the anharmonicity of the interatomic potentials of the atoms in the honeycomb lattice and thus can be used to verify theoretical models.Measurement of the strain dependence of the Raman active phonons is thus important for both applied and fundamental studies of this material system (12). By using graphene supported on a flexible substrate, we have been able to obtain precise information on the rate of frequency shift of the Raman G (zone-center optical) and 2D (two-phonon zone-edge optical) modes with strain. In addition, the polarization dependence of the Raman response in strained graphene can, as we demonstrate in this article, be used for an accurate determination of the crystallographic orientation. For unstrained graphene, such an orientation analysis is precluded by the high symmetry of the hexagonal lattice. A particularly important application of this capability lies in the study of nanopatterned graphene monolayers, such as nanoribbons (13) and quantum dots (14). Graphene nanoribbons possess electronic band gaps whose magnitude ref lects both the ribbon width and crystallographic orientation (13,(15)(16)(17). The electronic states associated with graphene edges are also sensitive to the crystallographic orientation of the ribbon (18). It is thus crucial to be able to correlate the measured properties to the underlying crystallographic orientation of the sample. As we show here, polarized Raman spectroscopy provides a simple, but precise analytic tool that complements electron-spectroscopy techniques such as scanning tunneling microscopy (STM) (19), transmission electron microscopy (TEM) (20), and low-energy electron diffraction (LEED) (21), methods that typically requ...

The optical transitions of semiconducting carbon nanotubes have been ascribed to excitons. Here we use two-photon excitation spectroscopy to measure exciton binding energies, as well as band-gap energies, in a range of individual species of semiconducting SWNTs. Exciton binding energies are large and vary inversely with nanotube diameter, as predicted by theory. Band-gap energies are significantly blue-shifted from values predicted by tight-binding calculations.

Time-resolved Raman spectroscopy has been applied to probe the anharmonic coupling and electron-phonon interaction of optical phonons in graphite. From the decay of the transient anti-Stokes scattering of the G-mode following ultrafast excitation, we measured a lifetime of 2.2 ± 0.1ps for zone-center optical phonons. We also observed a transient stiffening of G-mode phonons, an effect attributed to the reduction of the electron-phonon coupling for high electronic temperatures.Because of its intimate relation with nanotubes and graphene, graphite has recently attracted renewed attention. The interactions between its fundamental excitations --electron-electron, electron-phonon and phonon-phonon --play crucial roles in determining the basic physical properties of graphite. Ultrafast pump-probe spectroscopy, by permitting us to achieve non-equilibrium conditions, provides a powerful probe of these interactions [1][2][3][4][5]. Analysis of the dynamics indicates that optical phonons play an important or even dominant role in the relaxation of the excited system [3]. Further, an understanding of phonon dynamics and phonon-phonon interactions is crucial in defining high-field transport properties of graphitic materials [6,7].In this Letter, we present measurements of the ultrafast dynamics of phonons in graphite.Through application of femtosecond time-resolved Raman scattering [8,9], we trace the generation of non-equilibrium optical phonons by carrier cooling, their subsequent interaction with electronic excitations, and their decay through anharmonic coupling to lower-energy phonons. The experimental approach permits a direct determination of the absolute phonon mode population and its temporal evolution following femtosecond laser excitation. It complements a recent independent study by Ishioka et al. [10] in which ultrafast reflectivity measurements were used to trace the dynamics of coherent phonons in graphite. In our investigation we have established a broad understanding of the role of phonons in the ultrafast dynamics in graphite. We find that: (1) photo-excited carriers transfer most of their energy to a set of strongly-coupled optical phonons (SCOPs), including the zone-center (G-mode) phonons, 3 within a few hundred femtoseconds. This produces a significant non-equilibrium phonon population. The electronic excitations retain only a minor fraction of the initial excitation energy.(2) The optical phonons cool with a time constant of 2.2 ± 0.1 ps. Energy flows from the SCOPs to lower-energy phonons by anharmonic coupling. This process also cools the coupled electronic excitations in graphite. (3) In the transient regime, the non-equilibrium G-mode

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.

We report on the temperature dependence of the anharmonic decay rate of zone-center (G-mode) optical phonons in both single-walled carbon nanotubes and graphite. The measurements are performed using a pump-probe Raman scattering scheme with femtosecond laser pulses. For nanotubes, measured over a temperature range of 6 K -700 K, we observe little temperature dependence of the decay rate below room temperature. Above 300 K, the decay rate increases from 0.8 ps -1 to 1.7 ps -1 . The decay rates observed for graphite range from 0.5 to 0.8 ps -1 for temperatures from 300 -700 K.We compare the behavior observed in carbon nanotubes and graphite and discuss the implications of our results for the mechanism of the anharmonic decay of optical phonons in both systems.