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, ...
We report a comprehensive micro-Raman scattering study of electrochemically-gated graphene field-effect transistors. The geometrical capacitance of the electrochemical top-gates is accurately determined from dual-gated Raman measurements, allowing a quantitative analysis of the frequency, linewidth and integrated intensity of the main Raman features of graphene. The anomalous behavior observed for the G-mode phonon is in very good agreement with theoretical predictions and provides a measurement of the electron-phonon coupling constant for zone-center (Γ point) optical phonons. In addition, the decrease of the integrated intensity of the 2D-mode feature with increasing doping, makes it possible to determine the electron-phonon coupling constant for near zone-edge (K and K' points) optical phonons. We find that the electron-phonon coupling strength at Γ is five times weaker than at K (K'), in very good agreement with a direct measurement of the ratio of the integrated intensities of the resonant intra-(2D') and inter-valley (2D) Raman features. We also show that electrochemical reactions, occurring at large gate biases, can be harnessed to efficiently create defects in graphene, with concentrations up to approximately 1.4 × 10 12 cm −2 . At such defect concentrations, we estimate that the electron-defect scattering rate remains much smaller than the electron-phonon scattering rate. The evolution of the G-and 2D-mode features upon doping remain unaffected by the presence of defects and the doping dependence of the D mode closely follows that of its two-phonon (2D mode) overtone. Finally, the linewidth and frequency of the G-mode phonon as well as the frequencies of the G-and 2D-mode phonons in doped graphene follow sample-independent correlations that can be utilized for accurate estimations of the charge carrier density.
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