Using nanotubes to study the phonon spectrum of two-dimensional materials.

We propose a convenient method to characterize the acoustic phonon branches of 2D monolayer materials using measurements of the infrared- and Raman-active vibrational modes of nanotubes. The relations we employ are derived from a symmetry analysis based directly on the line groups of nanotubes. We perform extensive ab initio calculations for the MoS2 monolayer and nanotubes to evaluate the method and illustrate all our results. Specifically, we show how the low-energy phonon transmission, a determining factor in thermal transport, can be easily and successfully reconstructed by this procedure.