Valence Force Model for Phonons in Graphene and Carbon Nanotubes

Many calculations require a simple classical model for the interactions between sp^2-bonded carbon atoms, as in graphene or carbon nanotubes. Here we present a new valence force model to describe these interactions. The calculated phonon spectrum of graphene and the nanotube breathing-mode energy agree well with experimental measurements and with ab initio calculations. The model does not assume an underlying lattice, so it can also be directly applied to distorted structures. The characteristics and limitations of the model are discussed.Comment: 4 pages, 3 figure

Transforming carbon nanotubes by silylation: An ab initio study

We use ab initio density functional calculations to study the chemical functionalization of single-wall carbon nanotubes and graphene monolayers by silyl (SiH3) radicals and hydrogen. We find that silyl radicals form strong covalent bonds with graphene and nanotube walls, causing local structural relaxations that enhance the sp3 character of these graphitic nanostructures. Silylation transforms all carbon nanotubes into semiconductors, independent of their chirality. Calculated vibrational spectra suggest that specific frequency shifts can be used as a signature of successful silylation.Comment: 4 pages, 3 figure

Electron-Hole Asymmetry in Single-Walled Carbon Nanotubes Probed by Direct Observation of Transverse Quasi-Dark Excitons

We studied the asymmetry between valence and conduction bands in single-walled carbon nanotubes (SWNTs) through the direct observation of spin-singlet transverse dark excitons using polarized photoluminescence excitation spectroscopy. The intrinsic electron-hole (e-h) asymmetry lifts the degeneracy of the transverse exciton wavefunctions at two equivalent K and K' valleys in momentum space, which gives finite oscillator strength to transverse dark exciton states. Chirality-dependent spectral weight transfer to transverse dark states was clearly observed, indicating that the degree of the e-h asymmetry depends on the specific nanotube structure. Based on comparison between theoretical and experimental results, we evaluated the band asymmetry parameters in graphene and various carbon nanotube structures.Comment: 11 pages, 4 figure

Raman-scattering study of the phonon dispersion in twisted bi-layer graphene

Bi-layer graphene with a twist angle \theta\ between the layers generates a superlattice structure known as Moir\'{e} pattern. This superlattice provides a \theta-dependent q wavevector that activates phonons in the interior of the Brillouin zone. Here we show that this superlattice-induced Raman scattering can be used to probe the phonon dispersion in twisted bi-layer graphene (tBLG). The effect reported here is different from the broadly studied double-resonance in graphene-related materials in many aspects, and despite the absence of stacking order in tBLG, layer breathing vibrations (namely ZO' phonons) are observed.Comment: 18 pages, 4 figures, research articl

Mechanism of Near-Field Raman Enhancement in One-Dimensional Systems

We develop a theory of near-field Raman enhancement in one-dimensional systems, and report supporting experimental results for carbon nanotubes. The enhancement is established by a laser-irradiated nanoplasmonic structure acting as an optical antenna. The near-field Raman intensity is inversely proportional to the 10th power of the separation between the enhancing structure and the one-dimensional system. Experimental data obtained from single-wall carbon nanotubes indicate that the Raman enhancement process is not significantly influenced by the specific phonon eigenvector, and is mainly defined by the properties of the nanoplasmonic structure

Symmetry-derived selection rules for plasmon-enhanced Raman scattering

We show how to obtain the symmetry-imposed selection rules for plasmonic enhancement in surface- (SERS) and tip-enhanced Raman scattering (TERS). Plasmon-enhanced light scattering is described as a higher-order Raman process, which introduces a series of Hamiltonians representing the interaction between light, plasmons, electrons, and phonons. Using group theory, we derive the active representations for point group symmetries of exemplary plasmonic nanostructures. The phonon representations that are enhanced by SERS and TERS are then found as induced representations for the symmetry group of the molecule or another Raman probe. The selection rules are discussed for graphene that is coupled to a nanodisk dimer as an example for SERS and coupled to a tip as a TERS example. The phonon eigenmodes that are enhanced depend on the symmetry breaking when combining the plasmonic structures with graphene. We show that the most prominent optical phonon modes (E2g and A1g) are allowed in all scattering configurations when using a nanodimer as a plasmonic hotspot. We predict the activation of the silent B2g as well as infrared-active A2u and E1u modes in SERS for crossed configurations of the incoming and scattered light. There is a systematic difference between spatially coherent and incoherent plasmon-enhanced Raman scattering, which is responsible for a dependence of TERS on the phonon coherence length

Optical-phonon resonances with saddle-point excitons in twisted-bilayer graphene

Twisted-bilayer graphene (tBLG) exhibits van Hove singularities in the density of states that can be tuned by changing the twisting angle $\theta$. A $\theta$-defined tBLG has been produced and characterized with optical reflectivity and resonance Raman scattering. The $\theta$-engineered optical response is shown to be consistent with persistent saddle-point excitons. Separate resonances with Stokes and anti-Stokes Raman scattering components can be achieved due to the sharpness of the two-dimensional saddle-point excitons, similar to what has been previously observed for one-dimensional carbon nanotubes. The excitation power dependence for the Stokes and anti-Stokes emissions indicate that the two processes are correlated and that they share the same phonon.Comment: 5 pages, 6 figure

Group theory for structural analysis and lattice vibrations in phosphorene systems

Group theory analysis for two-dimensional elemental systems related to phosphorene is presented, including (i) graphene, silicene, germanene and stanene, (ii) dependence on the number of layers and (iii) two stacking arrangements. Departing from the most symmetric $D_{6h}^{1}$ graphene space group, the structures are found to have a group-subgroup relation, and analysis of the irreducible representations of their lattice vibrations makes it possible to distinguish between the different allotropes. The analysis can be used to study the effect of strain, to understand structural phase transitions, to characterize the number of layers, crystallographic orientation and nonlinear phenomena.Comment: 24 pages, 3 figure