Double-walled carbon nanotubes (DWNTs), often regarded as the simplest one-dimensional (1D) van der Waals moiré superlattices, are the ideal structures to explore the interlayer coupling, including mechanical and electronical coupling, at the nanoscale in 1D systems. By combining spatial modulation spectroscopy (SMS) and resonant Raman scattering (RRS) experiments on well-identified individual free-standing DWNTs with the calculations of their optical absorption by using the recursion method with non-orthogonal tight-binding (NTB) basis functions, we are able to unambiguously assign the nature, namely mirror transition or cross transition, of each optical transitions in DWNTs. Our study identifies and allows to determine the conditions of the mixing of the electronic states leading to the appearance of cross transitions in the optical absorption of DWNTs, beyond of the so-called Koshino's criteria previously derived. On the other hand, the striking behavior of the resonant excitation profile (REP) of the Raman active modes around the cross transition reveals the strong sensitivity of the modes intensity on the electronic interlayer coupling in DWNTs, emphasizing the relevance of Raman spectroscopy for studying the electronic and mechanical coupling at the nanoscale.

Polarized optical microscopy and spectroscopy are progressively becoming key methods for the high-throughput characterization of individual carbon nanotubes (CNTs) and other one-dimensional nanostructures, on substrate and in devices. The optical response of CNTs on substrate in cross polarization experiments is usually limited by the polarization conservation of the optical elements in the experimental setup. We developed a theoretical model taking into account the depolarization by the setup and the optical response of the substrate. We show that proper modelization of the experimental data requires to take into account both noncoherent and coherent light depolarization by the optical elements. We also show how the nanotube signal can be decoupled from the complex reflection factor of the antireflection substrate, which is commonly used to enhance the optical contrast. Finally, we describe an experimental protocol to extract the depolarization parameters and the complex nanotube susceptibility, and how it can improve the chirality assignment of individual carbon nanotubes in complex cases.

Double-walled carbon nanotubes (DWNTs), consisting of two coaxial and weakly van der Waals coupled single-walled carbon nanotubes (SWNTs), are one of the most ideal and fundamental systems to study the effects of inter-tube coupling on the physical properties in one-dimensional structures.On this poster, we report on the investigations of individual, spatially isolated and suspended double-walled carbon nanotubes (DWNTs) by combination of high-resolution electron microscopy, electron diffraction, Rayleigh spectroscopy and Raman spectroscopy (Figure 1) [1,2]. We first present an overview of the effect of the diameters, inter-tube distance and nature (metallic or semiconducting) on the Raman signature (Radial Breathing Like [1,3,4] and Tangential Modes [4-6]) of DWNTs. We then examine the features of tangential modes and find a clear frequency shift of the inner-layer G modes as a function of the inter-tube distance with respect to the corresponding G modes in equivalent single-walled carbon nanotubes (SWNT).[4-6] These results are understood by considering the effects of the relaxation of the layers and the interaction between the relaxed structures.[7] Finally, we study the experimental excitation dependence of the G modes intensity of the constituent inner and outer SWNTs. In particular, we discuss the effects of the quantum interference between different electronic transitions on the observed behaviors.[8]References[1] D.I. Levshov et al., Carbon, 114, 141 (2017). [2] D.I. Levshov et al., Phys Rev. B 96 (2017), 195410.[3] D.I. Levshov et al., Nano Lett. 11(11) (2011), 4800. [4] H.-N. Tran et al., Adv. Nat. Sci. Nanosci. Nanotechnol. (2017), 8, 15018.[5] D. Levshov et al., J. Phys. Chem. C 119(40) (2015), 23196.[6] D.I. Levshov et al., Phys. Status Solidi B 254(11) (2017), 1700251.[7] V.N. Popov et al., Phys. Rev. B 97 (2018), 165417.[8] H.-N. Tran et al., Phys. Rev. B 95 (2017), 95 (20), 205411

Using an experimental approach that combines high-resolution electron microscopy, electron diffraction and optical spectroscopies, including Raman scattering, Rayleigh spectroscopy and photoluminescence, on individual, spatially isolated and suspended (free-standing) single-walled (SWNTs) and double-walled carbon nanotubes (DWNTs), we have been able to investigate their phonons characteristics and optical properties. In this talk, we present an overview of the most significant results obtained via this approach. Particular attention is paid to the study of DWNTs, a coaxial composite of two SWNTs, which provide a unique model system for studying coupling at the nanoscale. We show how such coupling, originating from the van der Waals interaction between the inner and outer nanotubes, plays a crucial role in determining the characteristics of the collective radial breathing-like modes and G modes in DWNTs (for a review see Ref. 1-2). The effects of quantum interference between different electronic transitions on the experimental behavior of the G-modes intensity are discussed [3]. It must be emphasized that the theoretical predictions of Philippe Lambin and his collaborators have been invaluable in understanding a lot of these experimental data [4].