Unified Description of the Optical Phonon Modes in N-Layer MoTe2

N-layer transition metal dichalcogenides provide a unique platform to investigate the evolution of the physical properties between the bulk (three-dimensional) and monolayer (quasi-two-dimensional) limits. Here, using high-resolution micro-Raman spectroscopy, we report a unified experimental description of the Γ-point optical phonons in N-layer 2H-molybdenum ditelluride (MoTe2). We observe series of N-dependent low-frequency interlayer shear and breathing modes (below 40 cm–1, denoted LSM and LBM) and well-defined Davydov splittings of the mid-frequency modes (in the range 100–200 cm–1, denoted iX and oX), which solely involve displacements of the chalcogen atoms. In contrast, the high-frequency modes (in the range 200–300 cm–1, denoted iMX and oMX), arising from displacements of both the metal and chalcogen atoms, exhibit considerably reduced splittings. The manifold of phonon modes associated with the in-plane and out-of-plane displacements are quantitatively described by a force constant model, including interactions up to the second nearest neighbor and surface effects as fitting parameters. The splittings for the iX and oX modes observed in N-layer crystals are directly correlated to the corresponding bulk Davydov splittings between the E2u/E1g and B1u/A1g modes, respectively, and provide a measurement of the frequencies of the bulk silent E2u and B1u optical phonon modes. Our analysis could readily be generalized to other layered crystals