Interlayer Breathing and Shear Modes in Few-Trilayer\nMoS₂ and WSe₂

Abstract

Two-dimensional\n(2D) layered transition metal dichalcogenides (TMDs)\nhave recently attracted tremendous interest as potential valleytronic\nand nanoelectronic materials, in addition to being well-known as excellent\nlubricants in the bulk. The interlayer van der Waals (vdW) coupling\nand low-frequency phonon modes and how they evolve with the number\nof layers are important for both the mechanical and the electrical\nproperties of 2D TMDs. Here we uncover the ultralow frequency interlayer\nbreathing and shear modes in few-layer MoS₂ and WSe₂, prototypical layered TMDs, using both Raman spectroscopy\nand first principles calculations. Remarkably, the frequencies of\nthese modes can be perfectly described using a simple linear chain\nmodel with only nearest-neighbor interactions. We show that the derived\nin-plane (shear) and out-of-plane (breathing) force constants from\nexperiment remain the same from two-layer 2D crystals to the bulk\nmaterials, suggesting that the nanoscale interlayer frictional characteristics\nof these excellent lubricants should be independent of the number\nof layers.