Optically active cross-band transition in double-walled carbon nanotube and its impact on Raman resonances

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.
We acknowledge the Dr. T. X. Tinh for the synthesis of individual nanotubes. HNT, RP, AAZ, JLS and MP acknowledge financial support by the ANR GAMBIT project, grant ANR-13-BS10-0014 of the French Agence Nationale de la Recherche. The TEM studies were performed in the Laboratorio de Microscopias Avanzadas (LMA), Universidad de Zaragoza (Spain). R.A. acknowledges support from Spanish MICINN (PID2019-104739 GB-100/AEI/10.13039/501100011033), Government of Aragon (projects DGA E13-20R (FEDER, EU)) and from EU H2020 “ESTEEM3” (Grant number 823717). VNP acknowledges financial support for NTB calculations from the National Science Fund of Bulgaria under grant KP-06-N38/10 from December 06, 2019.