Stacking-dependent interlayer phonons in 3R and 2H MoS₂

Atomically thin MoS₂, a prototype two-dimensional semiconductor, commonly exhibits the 2H stacking order. In even layer numbers, 2H MoS₂ restores the inversion symmetry and hence loses many attractive properties, such as second harmonic generation, piezoelectricity and spin-valley coupling.But researchers have recently grown MoS₂ crystals with 3R stacking order, which in all layer numbers breaks the inversion symmetry and retains the valleytronic, piezoelectric and nonlinear optical properties as in the monolayer.
We have directly probed the stacking-dependent interlayer coupling in the pure 2H and 3R structure of MoS₂ by ultralow-frequency Raman spectroscopy. We observe up to three shear branches and four breathing branches in MoS₂ samples with thickness from 2 to 13 layers. Our results show distinct behavior of the shear modes between 2H and 3R MoS₂, and also suggest a slightly enhanced interlayer coupling in 2H MoS₂ compared to 3R MoS_2. Through a combination first-principles calculations, group theory, and an effective bond-polarizability model, we account for all the major observations in our experiment.