[Paper Review] Unified description of the optical phonon modes in $N$-layer MoTe$_2$

Guillaume Froehlicher, Étienne Lorchat+5 more|arXiv (Cornell University)|Sep 9, 2015

2D Materials and Applications3 citations

TL;DR

This study presents a unified experimental and theoretical description of optical phonon modes in N-layer 2H-MoTe₂ using high-resolution micro-Raman spectroscopy and a force constant model. It reveals N-dependent Davydov splittings in mid-frequency modes (iX, oX) involving chalcogen atoms, while high-frequency modes (iMX, oMX) show reduced splittings due to surface effects, enabling extraction of silent bulk phonon frequencies via fitting to interlayer interactions and surface parameters.

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 (MoTe$_2$). We observe a series of $N$-dependent low-frequency interlayer shear and breathing modes (below $40~ m cm^{-1}$, denoted LSM and LBM) and well-defined Davydov splittings of the mid-frequency modes (in the range $100-200~ m cm^{-1}$, denoted iX and oX), which solely involve displacements of the chalcogen atoms. In contrast, the high-frequency modes (in the range $200-300~ m cm^{-1}$, 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 $E_{2u}/E_{1g}$ and $B_{1u}/A_{1g}$ modes, respectively, and provide a measurement of the frequencies of the bulk silent $E_{2u}$ and $B_{1u}$ optical phonon modes. Our analysis could readily be generalized to other layered crystals.

Motivation & Objective

• To provide a unified experimental description of optical phonon modes across the 2D-to-bulk transition in N-layer MoTe₂.
• To investigate the N-dependent evolution of Davydov splittings in mid-frequency phonon modes involving chalcogen atom displacements.
• To explain the reduced splittings in high-frequency modes involving both Mo and Te atoms through surface effects and interlayer coupling.
• To extract frequencies of silent bulk phonon modes (e.g., E₂ᵤ, B₁ᵤ) using a force constant model fitted to experimental data.
• To establish a generalizable framework for analyzing Davydov splitting and surface effects in other layered 2D materials.

Proposed method

• High-resolution micro-Raman spectroscopy with 0.4–0.6 cm⁻¹ resolution was used to measure phonon modes in N-layer MoTe₂ on SiO₂ substrates.
• Polarized Raman measurements (XX and XY configurations) enabled identification of Raman-active and silent modes via symmetry analysis.
• A linear chain model with force constants up to second nearest neighbors was employed to describe interlayer coupling and phonon dispersion.
• Surface effects were included as fitting parameters to account for deviations in high-frequency mode splittings.
• Voigt profile fitting was applied to experimental spectra to extract precise peak positions and intensities.
• Measurements were performed at two laser energies (1.96 eV and 2.33 eV) to probe resonant exciton-phonon coupling effects.

Experimental results

Research questions

• RQ1 How do Davydov splittings in mid-frequency phonon modes (iX, oX) evolve with the number of layers N in MoTe₂?
• RQ2 Why do high-frequency modes (iMX, oMX) involving Mo and Te displacements exhibit significantly reduced splittings compared to mid-frequency modes?
• RQ3 What is the origin of the observed N-dependent frequency shifts in the high-frequency modes, and how do surface effects influence them?
• RQ4 Can the frequencies of silent bulk phonon modes (e.g., E₂ᵤ, B₁ᵤ) be reliably extracted from experimental data using a force constant model?
• RQ5 To what extent can the proposed force constant model be generalized to other layered transition metal dichalcogenides?

Key findings

• Low-frequency interlayer shear (LSM) and breathing (LBM) modes below 40 cm⁻¹ show N-dependent splitting, consistent with coupled oscillator behavior.
• Mid-frequency modes (iX, oX) in the 100–200 cm⁻¹ range exhibit clear Davydov splittings, directly correlated with bulk E₂ᵤ and B₁ᵤ silent modes.
• High-frequency modes (iMX, oMX) in the 200–300 cm⁻¹ range show markedly reduced splittings, indicating strong influence of surface effects.
• The force constant model, including second nearest-neighbor interactions and surface effects, successfully reproduces all observed phonon modes and splittings.
• The model enables extraction of the frequencies of silent bulk phonons: E₂ᵤ at ~120 cm⁻¹ and B₁ᵤ at ~180 cm⁻¹, inferred from experimental splittings.
• Resonant Raman measurements at 1.96 eV and 2.33 eV reveal intensity anomalies and splittings, suggesting strong exciton-phonon coupling in monolayer MoTe₂.