We present experimental measurements of the features of G band in individual index-identified free-standing double-walled carbon nanotubes. We examine Raman spectra of different electronic configurations of DWNTs, namely: SC@SC, SC@M, M@SC, M@M, and clearly establish that, as in SWNTs, the profile of LO G-mode of each layer is broad (narrow) when the layer is metallic (semiconducting). The dependence of G-modes on thediameter and inter-layer distance in several SC@SC, SC@M, M@SC, M@M index-identified DWNTs is reported. We find, that, independently of the metallic or semiconducting nature of the layers, the frequencies of LO and TO G-mode of the inner and outer layers shift significantly with respect to the frequencies of the same modes in the constituent SWNTs.

We report direct and unambiguous evidence of the existence of inner semiconducting tube (ISCT) photoluminescence (PL) from measurements performed on four individual freestanding index-identified double-walled carbon nanotubes (DWNTs). Based on thorough Rayleigh scattering, Raman scattering, and PL experiments, we are able to demonstrate that the ISCT PL is observed with a quantum yield estimated to be a few 10−6 independent of the semiconducting or metallic nature of the outer tube. This result is mainly attributed to ultrafast exciton transfer from the inner to outer tube. Furthermore, by carrying out PL excitation experiments on the (14,1)@(15,12) DWNT, we show that the ISCT PL can be detected through the optical excitation of the outer tube, indicating that the exciton transfer can also occur in the opposite way.

The effects of quantum interferences on the excitation dependence of the intensity of G modes have beeninvestigated on single-walled carbon nanotubes [Duque et al., Phys. Rev. Lett. 108, 117404 (2012)]. In this work,by combining optical absorption spectroscopy and Raman scattering on individual index identified double-walledcarbon nanotubes, we examine the experimental excitation dependence of the intensity of longitudinal opticaland transverse optical G modes of the constituent inner and outer single-walled carbon nanotubes. The observedstriking dependencies are understood in terms of quantum interference effects. Considering such effects, the excitation dependence of the different components of the G modes permits us to unambiguously assign each ofthem as originating from the longitudinal or transverse G modes of inner and outer tubes.

The experimental approach combining high resolution transmission electron microscopy (HRTEM), electron diffraction (ED) and resonant Raman spectroscopy (RRS) on the same free-standing individual carbon nanotubes (CNT) is the most efficient method to determine unambiguously the intrinsic features of the Raman-active phonons. In this paper, we review the main results obtained by the approach regarding the intrinsic features of the phonons of single-walled (SWNT) and double-walled carbon nanotubes (DWNT). First, we detail the different methods to identify the structure of SWNTs and DWNTs from the analysis of their electron diffraction patterns (EDP). In the following, we remind the principal features of the Raman response of SWNTs, unambiguously index-identified by ED. A special attention is devoted to the effect of the inter-layer interaction on the frequencies of the Raman-active phonons in index-identified DWNTs. The information obtained on index-identified SWNT and DWNT allows us to propose Raman criteria, which help identifying CNT when the ED fails to propose a single assignment. The efficiency of the Raman criteria as the complement to the ED information for the index-assignment of a few SWNTs and DWNTs is shown. The same approach to index-assign a triple-walled carbon nanotube (TWNT), by combining ED and RRS information, is reported.

We examine the excitonic nature of the E33 optical transition of the individual free-standing index-identified(23,7) single-walled carbon nanotube by means of the measurements of its radial-breathing-mode and G-modeRaman excitation profiles. We confirm that it is impossible to determine unambiguously the nature of its E33optical transition (excitonic vs band to band) based only on the excitation profiles. Nevertheless, by combiningRaman scattering, Rayleigh scattering, and optical absorption measurements on strictly the same individual(23,7) single-walled carbon nanotube, we show that the absorption, Rayleigh spectra, and Raman excitationprofiles of the longitudinal and transverse G modes are best fitted by considering the nature of the E33 transitionas excitonic. The fit of the three sets of data gives close values of the transition energy E33 and damping parameter. This comparison shows that the fit of the Raman excitation profiles provides with good accuracy the energy and damping parameter of the excitonic optical transitions in single-walled carbon nanotubes.

In this paper, we present an alternative way to study theoretically low-frequency collective modes of DWNTs based on the continuous 2D membrane theory. We obtain aωRBLM (do , di) relation being an equivalent of the conventional formulas established for individual SWNTs. We compare our theoretical predictions with Raman data measured on individual index-identified suspended DWNTs. A good agreement between the experiment and the predictions of the continuous theory is found. We show that the coupling in individual DWNTs strongly depends on the interlayer distance, which is manifested in the frequency shifts of the radial breathing-like modes (RBLMs) with respect to the radial breathing modes (RBM) of the individual inner and outer tubes. In terms of characterization, the combination of Ramanspectroscopy data and the predictions of continuous membrane theory may give additional criteria for the index-identification of DWNTs.