Interlayer Breathing and Shear Modes in Few-Trilayer MoS₂ and WSe₂

Abstract

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

Gate‐Tunable Resonant Raman Spectroscopy of Bilayer MoS2

“…Quantitatively, the frequency of two identical coupled oscillator ω 1 (A 1g in bilayer) can be determined by 0 2 2 ω ϖ + ∆ , where ω 0 represents the frequency of the isolated oscillator (A 1g in monolayer, i.e., A′ 1 ) and Δω is related to the interlayer coupling (the interlayer breathing mode of bilayer, ≈39.5 cm −1 in 2H-MoS 2 ). [10] This analysis shows good agreement with the experimentally measured Raman shift in MoS 2 . [10,27] When ω 1 decreases upon changing the excitation laser from 514.5/532 to 633 nm, the possibilities are either ω 0 or Δω becomes smaller (or both).…”

“…[10] This analysis shows good agreement with the experimentally measured Raman shift in MoS 2 . [10,27] When ω 1 decreases upon changing the excitation laser from 514.5/532 to 633 nm, the possibilities are either ω 0 or Δω becomes smaller (or both). While excitation of 532 nm (2.33 eV) is in resonant to peak C (a broad peak ranging from 2.2 to 2.8 eV) in the absorption spectra of MoS 2 .…”

“…[7] Raman spectroscopy is a versatile probe in studying the crystalline and vibrational properties of TMDs. [8][9][10][11][12] Gatetunable phonon properties in graphene, [13,14] MoS 2 , [15] and black phosphorus [16] have also been reported. With a gateinduced electron doping, the out-of-plane A 1g mode in mono layer MoS 2 is down-shifted while the in-plane vibrational mode E 2g 1 does not show observable change.…”

Resonant Raman spectroscopy of twisted multilayer graphene

“…However, their intensity, I(C), is much smaller than that of the G peak, I(G), because of the much lower electron-phononcoupling (EPC) 18 , and it is smaller the lower the Pos(C), for a given N. Thus, so far, the lower energy C modes for a given N could not be detected 18 . Similar C modes exist in any other layered material 18,25 , but their intensity is comparable to that of the main high-frequency Raman peaks, allowing for the detection of some of the possible N-1 C modes for a given N 25,26 , not just the highest energy one. Note that, albeit being an overtone of an in-plane mode, the 2D peak is sensitive to N since the resonant Raman mechanism that gives rise to it is closely linked to the details of the band structure 4,15,17 , the latter changing with N, and the layers relative orientation 15 .…”

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

“…Molybdenum disulfide (MoS 2 ), a prototypical example of TMDs, is a layered system where Mo atoms form hexagonal layers 2,3 . Each of the Mo hexagonal layers is sandwiched between two similar lattices of S atoms, forming a trilayer 4,5 . The atoms within each trilayer are held together by strong covalent bonds, while the trilayers of MoS 2 interact primarily through weak van der Waals interactions.…”