Two-dimensional elasticity determines the low-frequency dynamics of single- and double-walled carbon nanotubes

Abstract

We develop a continuous theory of low-frequency dynamics for nanotubes with walls constituted by single-atom monolayer, the topological elasticity of which is not related to its vanishing macroscopic thickness. The applicability region of the theory proposed includes all truly two-dimensional materials such as graphene and MoS2. New comprehensive interpretation and analytical expressions for low-frequency modes in single-walled carbon nanotube (SWCNT) are given. The theory unambiguously relates the radial breathing modes of SWCNT and breathinglike modes of the double-walled carbon nanotube (DWCNT). The existing Raman data on DWCNTs are fitted better than in the frame of previous models. © 2013 American Physical Society.