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 a 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.Keywords: Two-dimensional materials, layered crystals, transition metal dichalcogenides, MoTe2, Raman spectroscopy, interlayer breathing and shear modes, force constants, Davydov splitting, surface effects.Introduction In the wake of graphene, a vast family of layered materials is attracting tremendous attention [1]. Now available in the form of N -layer crystals, the latter exhibit peculiar physical properties that complement the assets of graphene and offer exciting perspectives to design van der Waals heterostructures [1]. Semiconducting transition metal dichalcogenides (MX 2 , with M = Mo, W and X = S, Se, Te) are among the most actively investigated layered crystals [2]. Indeed, although bulk MX 2 exhibit indirect bandgaps, monolayer MX 2 are direct bandgap semiconductors [3,4] with remarkable spin, valley [5] and optoelectronic properties [6]. More Generally, N -layer MX 2 crystals provide an ideal platform to uncover the impact of symmetry breaking and interlayer interactions on the electronic, optical and vibrational properties, from the bulk (three-dimensional) to the monolayer (quasi two-dimensional) limit.In particular, in N -layer MX 2 , interlayer interactions result in a splitting of all the monolayer phonon modes [7][8][9][10][11][12][13][14][15][16] (see Table I). The latter effect is known as the Davydov splitting [17] and is closely related to the force constants that govern the vibrational properties of MX 2 [9]. The Davydov splitting has been previously studied in polyaromatic molecules [18], thin films [19], and bulk layered crystals, ...

Resonance effects in the Raman scattering of monolayer and few-layerMoSe2

“…3c). Indeed, as already reported 22 , this peak has an energy that depends on the number of layers, appears in the Raman scattering spectrum as a single component feature for 1L-MoSe 2 and 2L-MoSe 2 , splits into two components for 3L-MoSe 2 and 4L-MoSe 2 and into three 20,29,43 , can be used to determine the number of layers. Close to 252 cm −1 , another Raman scattering feature is observed with an energy that changes with the number of layer.…”

“…Similar to the TO E'/E g at 289 cm −1 and to the A" 2 /A 1g mode at 354 cm −1 , the breathing mode's intensity seems to show a resonance with electronic excitations above the energy of the C exciton. For different MX 2 materials, depending on the excitation laser and on the exciton energy structure, very different intensity ratios between the shear and breath modes have been reported recently 19,29,34,35,44 . As follows from the study reported here, these differences arise from the peculiar resonance effect affecting differently the two modes.…”

Quantum Effects and Phase Tuning in Epitaxial Hexagonal and Monoclinic MoTe2 Monolayers

“…[1,8] They have attracted extensive research attention in recent years due to their appeals in microelectronic, optoelectronic, spin and valley electronic applications. [1,9,10,11,12] The 1T' or Td phase MX 2 are of the distorted 1T structure, which usually show semi-metallic behavior. [3,[13][14][15] Examples of the latter include WTe 2 and -MoTe 2 , which have drawn special interests lately following some recent revelations of, e.g., the large and unsaturated magnetoresistance, [4,15,16,17,18] pressure-driven superconductivity, [7,19] novel optical properties and characteristics, [11,12,17,18,20] and the topological insulator [14] and Weyl semimetal states.…”

Apparent breakdown of Raman selection rule at valley exciton resonances in monolayerMoS2

“…Here, we investigate its effect on Raman scattering. Raman spectroscopy has been used extensively on 2D materials, such as graphene and TMDC's, for studying thicknessdependent properties [13][14][15][16][17][18][19][20] and probing strain effects [21,22]. However, few Raman studies have examined systematically the polarization selection rule for TMDCs with circularly polarized excitation and detection [23].…”