Two-phonon Raman bands of single-walled carbon nanotubes: A case study

Abstract

It has been long accepted that the second-order Raman bands in carbon nanotubes are enhanced through the double-resonance mechanism. Although separate aspects of this mechanism have been studied for a few second-order Raman bands, including the most intense defect-induced D band and the two-phonon 2D band, a complete computational approach to the second-order bands is still lacking. Here, we propose such an approach, entirely based on a symmetry-adapted non-orthogonal tight-binding model with ab-initio-derived parameters. As a case study, we consider nanotube (6, 5), for which we calculate the two-phonon spectrum. We investigate in detail the 2D band and identify three contributions to it: a non-dispersive one and two dispersive ones, which are found to depend on the electron and phonon dispersion of the nanotube, and on the laser excitation. We also predict two-phonon bands, which are not allowed in the parent structure graphene. The obtained two-phonon bands are in very good agreement with the available experimental data. The symmetry-adapted formalism makes feasible the calculation of the two-phonon Raman bands of any observable nanotube.

Electroluminescence from Single-Walled Carbon Nanotubes with Quantum Defects

“…We note that the RBM bandwidth is found to scale inversely with the unit cell size, 51 and for the chiral (6, 5) and (7, 5) nanotubes with large unit cells, the RBM bandwidth is expected to be small. In the case of the (6, 5) nanotube, the RBM frequency, calculated within a tight-binding model, shows only a slight variation of about 1% throughout the Brillouin zone of the nanotube, 52 and therefore the RBM bandwidth is small enough to consider the RBM frequency as a constant. To identify the piece of the RBM branch, relevant to the relaxation processes, we use the E 11 exciton mass, derived within a tight-binding model, and find that the exciton states in the energy range from E* to E 11 (Figure 5b) have wavevectors in the first Brillouin zone.…”

Investigation of Electrochemical Charge Storage Efficiency of NiCo2Se4/RGO Composites Derived at Varied Duration and Its Asymmetric Supercapacitor Device

“…NCRG-12 and NCRG-18 showed an intense 2D peak at ∼2695 cm –1 . However, the intensity of the 2D peak decreased significantly and broadened in NCRG-6, suggesting the agglomeration of RGO sheets in NCRG-6. ,,– The Raman spectra of NCSRGs (Figure d) showed a blue shift in the G band compared to the NCRG materials. This anomaly may be due to the increasing number of defects in the presence of Se.…”

“…The peak positions of all of the three NCSRG materials are located almost in the same position, but differed by their intensity, suggesting the change in structural transformation with duration of hydrothermal reaction. The average crystalline size of the three NCSRG electrode materials was determined from the Scherrer equation (eq ) considering the (101), (102), (110), (103), and (112) diffraction peaks. , where D , λ, β, and θ are the crystalline size, wavelength, full width at half-maximum (FWHM), and diffraction angle, respectively. The average crystallite sizes for NCSRG-6, NCSRG-12, and NCSRG-18 were found to be 0.189, 0.193, and 0.156 nm, respectively.…”