Resonance Raman spectroscopy(n,m)-dependent effects in small-diameter single-wall carbon nanotubes

Abstract

This paper presents an accurate analysis of ͑i͒ the electronic transition energies E 22 S and E 11 M , ͑ii͒ the radial breathing mode ͑RBM͒ frequencies RBM , and ͑iii͒ the corresponding RBM intensities from 40 small-diameter single-wall carbon nanotubes ͑SWNTs͒ in the diameter range 0.7Ͻ d t Ͻ 1.3 nm. The electronic transition energies ͑E ii ͒ are initially considered from nonorthogonal tight-binding total-energy calculations. To account for d t -dependent many-body effects, a logarithmic correction, as proposed by Kane and Mele, is applied to both E 22 S and E 11 M . The remaining discrepancies between the experimental and theoretical E ii values are shown to beproportional to the chirality-dependent effective masses of electrons and holes, as obtained from the electron energy dispersion relations. Chirality dependent screening effects are also identified in metallic SWNTs. For the RBM frequencies, a small deviation from the linear 1 / d t behavior is observed, and this deviation is analyzed based on a chirality-dependent mode softening effect due to nanotube curvature. For those interested in sample characterization, the ͑n , m͒ dependence of the resonance intensities is also addressed, the experimental results being compared with theoretical predictions based on matrix elements calculations. This analysis suggests that the ͑7,5͒, ͑7,6͒, and ͑6,5͒ SWNTs are more abundant in sodium dodecyl sulfate wrapped HiPco SWNTs in aqueous solution, in agreement with results previously reported for SWNTs grown by the CoMoCAT or alcohol methods.

Wall-to-wall stress induced in (6,5) semiconducting nanotubes by encapsulation in metallic outer tubes of different diameters: A resonance Raman study of individual C60-derived double-wall carbon nanotubes

“…3 shows that, when using E laser =2.08 and 2.10eV, we excited the E S 22 transitions of (6,5) inner semiconducting tubes and the E M 11 transitions of outer metallic tubes mainly from family 2n+m=33. The Kataura plot was calculated within the ETB (extended tight binding) framework [17], including manybody corrections, fitted to the RRS (resonance Raman scattering) data from sodium docecyl sulfate-wrapped HiPCO (High Pressure CO conversion) SWNTs [18]. We find that such a Kataura plot (Fig.…”

Resonance Raman spectroscopy in one-dimensional carbon materials

“…Here we obtained (E ii , ω RBM ) for 46 different (n, m) SWNTs, including 28 semiconducting and 18 metallic SWNTs. These studies allowed the development of more reliable models to describe the detailed electronic structure of SWNTs, including effects due to SWNT curvature and related to (2n + m) family behavior, as well as many-body effects (Samsonidze et al 2004, Jorio et al 2005. Furthermore, through these measurements, the important equivalence was demonstrated between the optical transition energies E ii obtained by resonance Raman spectroscopy and photoluminescence excitation (PLE) spectroscopy (O'Connell et al 2002).…”

Fundamental optical processes in armchair carbon nanotubes

“…Subsequent studies by Doorn et al, 94 Telg et al, 95 Fantini et al, 96 and Maultzsch et al 97 on surfactant-suspended HiPco nanotubes and later surfactant-suspended CoMoCAT nanotubes, 98 correctly assigned RBM features using optical transition energies obtained from Raman excitation profiles to (n, m) species. The combined data sets of tabulated (n, m) with RBM frequencies and optical transition energies allowed Maultzsch et al 97 and also Jorio et al 99 to develop empirical equations to predict both RBM frequencies and optical transition energies for nanotubes, which has served as an experimental predictive tool for locating previously unobserved spectral features. 100 Jorio et al, 99 in particular, attempted to take existing expressions for tight-binding calculations predicting SWCNT optical transitions and add additional chiral-angle-dependent and logarithmic terms to account for chiral-dependent electron and hole effective masses and many-body corrections, respectively, with parameters tuned to fit existing optical data.…”