Two-dimensional (2D) layered transition metal dichalcogenides (TMDs) have recently attracted tremendous interest as potential valleytronic and nanoelectronic materials, in addition to being well-known as excellent lubricants in the bulk. The interlayer van der Waals (vdW) coupling and low-frequency phonon modes and how they evolve with the number of layers are important for both the mechanical and the electrical properties of 2D TMDs. Here we uncover the ultralow frequency interlayer breathing and shear modes in few-layer MoS2 and WSe2, prototypical layered TMDs, using both Raman spectroscopy and first principles calculations. Remarkably, the frequencies of these modes can be perfectly described using a simple linear chain model with only nearest-neighbor interactions. We show that the derived in-plane (shear) and out-of-plane (breathing) force constants from experiment remain the same from two-layer 2D crystals to the bulk materials, suggesting that the nanoscale interlayer frictional characteristics of these excellent lubricants should be independent of the number of layers.

Realizing Raman enhancement on a flat surface has become increasingly attractive after the discovery of graphene-enhanced Raman scattering (GERS). Two-dimensional (2D) layered materials, exhibiting a flat surface without dangling bonds, were thought to be strong candidates for both fundamental studies of this Raman enhancement effect and its extension to meet practical applications requirements. Here, we study the Raman enhancement effect on graphene, hexagonal boron nitride (h-BN), and molybdenum disulfide (MoS2), by using the copper phthalocyanine (CuPc) molecule as a probe. This molecule can sit on these layered materials in a face-on configuration. However, it is found that the Raman enhancement effect, which is observable on graphene, hBN, and MoS2, has different enhancement factors for the different vibrational modes of CuPc, depending strongly on the surfaces. Higher-frequency phonon modes of CuPc (such as those at 1342, 1452, 1531 cm(-1)) are enhanced more strongly on graphene than that on h-BN, while the lower frequency phonon modes of CuPc (such as those at 682, 749, 1142, 1185 cm(-1)) are enhanced more strongly on h-BN than that on graphene. MoS2 demonstrated the weakest Raman enhancement effect as a substrate among these three 2D materials. These differences are attributed to the different enhancement mechanisms related to the different electronic properties and chemical bonds exhibited by the three substrates: (1) graphene is zero-gap semiconductor and has a nonpolar C-C bond, which induces charge transfer (2) h-BN is insulating and has a strong B-N bond, while (3) MoS2 is semiconducting with the sulfur atoms on the surface and has a polar covalent bond (Mo-S) with the polarity in the vertical direction to the surface. Therefore, the different Raman enhancement mechanisms differ for each material: (1) charge transfer may occur for graphene; (2) strong dipole-dipole coupling may occur for h-BN, and (3) both charge transfer and dipole-dipole coupling may occur, although weaker in magnitude, for MoS2. Consequently, this work studied the origin of the Raman enhancement (specifically, chemical enhancement) and identifies h-BN and MoS2 as two different types of 2D materials with potential for use as Raman enhancement substrates.

We have studied the optical transition energies of single-wall carbon nanotubes over broad diameter (0.7-2.3 nm) and energy (1.26-2.71 eV) ranges, using their radial breathing mode Raman spectra. We establish the diameter and chiral angle dependence of the poorly studied third and fourth optical transitions in semiconducting tubes. Comparative analysis between the higher lying transitions and the first and second transitions show two different diameter scalings. Quantum mechanical calculations explain the result showing strongly bound excitons in the first and second transitions and a delocalized electron wave function in the third transition.

Resonance Raman scattering is used to determine the radial breathing mode ͑RBM͒ frequency ͑ RBM ͒ dependence on tube diameter ͑d t ͒ for single-wall carbon nanotubes ͑SWNTs͒. We establish experimentally the RBM = 227.0/ d t as the fundamental relation for pristine SWNTs. All the other RBM values found in the literature can be explained by an upshift in frequency due mostly to van der Waals interaction between SWNTs and environment. DOI: 10.1103/PhysRevB.77.241403 PACS number͑s͒: 78.67.Ch, 71.35.Ϫy, 73.22.Ϫf, 78.30.Na The radial breathing mode ͑RBM͒ provides the spectroscopic signature of single-wall carbon nanotubes ͑SWNTs͒.1,2 The RBM frequency ͑ RBM ͒ depends on the SWNT diameter ͑d t ͒, which is related to their ͑n , m͒ struc-The experimental results in the literature have been fitted with the relation RBM = A / d t + B, with values for A and B varying from paper to paper. [3][4][5][6][7][8][9][10][11][12] The empirical constant factor B prevents the expected limit of a graphene sheet from being achieved, where the RBM should go to zero when d t approaches infinity. Therefore, B is supposedly associated with an environmental effect on RBM , rather than an intrinsic property of SWNTs. Environmental effect here means the effect of the surrounding medium, such as bundling, molecules adsorbed from the air, surfactant used for SWNT bundle dispersion, and substrates where the tubes are sitting.Here we use resonance Raman scattering to measure the RBMs of SWNTs grown by the water-assisted chemical vapor deposition ͑CVD͒ method. [13][14][15][16] These SWNTs follow a simple linear relation between RBM and d t , with the proportionality constant A = 227.0 cm −1 nm, in agreement with the elastic property of graphite, and with a negligible environmental effect ͑B Ϸ 0͒. All the observed RBM reported in the literature are upshifted from this fundamental relation. 3-12The upshift exhibits a d t dependence in quantitative agreement with recent predictions considering the van der Waals interaction between SWNTs and environment. 17This water-assisted CVD process has been called "supergrowth" and generates millimeter-long isolated and highpurity SWNTs. [13][14][15][16] The super-growth SWNTs exhibit a broad d t distribution ͑d t from 1 to 4 nm͒ and all tube chiralities ͑0°Յ Յ 30°͒. The SWNTs are vertically aligned from a silicon substrate to form a very sparse material, where SWNTs represent only 3.6% of the total volume.15 Two triple-monochromator Raman spectrometers ͑a Dilor XY in the visible and a SPEX in the near-infrared͒ with charge coupled device ͑CCD͒ detectors are used to acquire the spectra. In both cases a backscattering geometry is applied. An Ar-Kr laser and two quasicontinuous ͑dye and Ti:sapphire͒ lasers are used to tune the excitation laser wavelength. The laser power density is maintained constant, low enough to avoid heating effects ͑1 mW focused with an 80ϫ objective in the visible, and 25 mW focused with a 10 cm focal length in the infrared͒.In Fig. 1 we compared similar RBM Raman spectra of two differen...

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