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.