title: Unified Description of the Optical Phonon Modes in N-Layer MoTe2.
abstract: 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.
authors.affiliation: Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Lœss, BP43, 67034 Strasbourg Cedex 2, France.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Froehlicher
authors.affiliation: Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Lœss, BP43, 67034 Strasbourg Cedex 2, France.
authors.forename: Etienne
authors.initials: E
authors.lastname: Lorchat
authors.affiliation: Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Lœss, BP43, 67034 Strasbourg Cedex 2, France.
authors.forename: François
authors.initials: F
authors.lastname: Fernique
authors.affiliation: Physics and Materials Science Research Unit, University of Luxembourg , 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg.|Department of Physics, Indian Institute of Technology Bombay , Powai, Mumbai 400076, India.
authors.forename: Chaitanya
authors.initials: C
authors.lastname: Joshi
authors.affiliation: Physics and Materials Science Research Unit, University of Luxembourg , 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg.
authors.forename: Alejandro
authors.initials: A
authors.lastname: Molina-Sánchez
authors.affiliation: Physics and Materials Science Research Unit, University of Luxembourg , 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg.
authors.forename: Ludger
authors.initials: L
authors.lastname: Wirtz
authors.affiliation: Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Lœss, BP43, 67034 Strasbourg Cedex 2, France.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Berciaud
keywords: Davydov splitting; MoTe2; Raman spectroscopy; force constants; interlayer breathing and shear modes; layered crystals; surface effects; transition metal dichalcogenides; two-dimensional materials