Lattice dynamics of the charge density wave compounds TaTe$_4$ and NbTe$_4$ and their evolution across solid solutions

Abstract

Understanding lattice dynamics is central to elucidating the microscopic origin of charge density waves (CDWs), particularly in materials where electron-phonon coupling can play a dominant role. Raman spectroscopy, combined with first-principles calculations, offers a direct means to identify the vibrational modes involved and to monitor their evolution under controlled perturbations. In this work, we combine density functional theory calculations and Raman spectroscopy measurements to investigate the vibrational properties of the quasi-one-dimensional transition metal tetrachalcogenides TaTe$_4$ and NbTe$_4$, as well as their solid solutions Ta$_{1-x}$Nb$_{x}$Te$_4$ ($x$ = 0.0 - 1.0). For the stoichiometric compounds, first-principles calculations predict a phonon instability consistent with the trimerization associated with the CDW phase, providing theoretical evidence for the lattice distortion driving the transition. The calculated Raman-active modes show good agreement with room-temperature experimental spectra, enabling a systematic assignment of the observed peaks. Across the solid solution, most Raman modes evolve smoothly with composition. In contrast, the highest-frequency E$_{g}$ mode, dominated by transition-metal motion, exhibits a distinct behavior: its frequency remains close to that of the parent compounds while its intensity redistributes with stoichiometry. This evolution highlights the short-range character of this vibrational mode and suggests its relevance to the CDW-related lattice distortion in these materials.

Figures (4)

• Figure 1: (a) (Color online) Crystalline structure of $M$Te$_{4}$, with $M$ = Ta or Nb, alongside their first Brillouin zone in the $P4/mcc$ (SG. 124), or high-temperature non-CDW phase. (b) Crystalline structure of $M$Te$_{4}$ in its CDW phase, which corresponds to the $P4/ncc$ (SG. 130) low-temperature phase. The picture highlights the trimerization of the transition metal along the chains, and the A--B--A stacking of the chains once the commensurate CDW is condensed. (c) Full phonon dispersion curves computed for NbTe$_{4}$ and (d) and TaTe$_{4}$ at 0 K. The unstable phonon modes close to the A point are denoted at negative frequency values by notation. Similarly, (e) and (f) show the full phonon dispersion curves at 300 K for NbTe$_{4}$ and TaTe$_{4}$, respectively. Here, the Nb, Ta, and Te sites are denoted in green, blue, and dark olive, respectively, both at the unit cell representations and to indicate phonon bands that are dominated by respective atom motion.
• Figure 2: (Color online) (a) Raman spectroscopy measurements performed at room temperature for NbTe$_{4}$ and (b) TaTe$_{4}$, and their comparison with theoretical predictions at both 0 K and 300 K. Solid (dashed) vertical lines represent the calculated positions for the 0 K (300 K) modes. The different colors used represent the different irreps at the $\Gamma$ high-symmetry point of each of the predicted modes: blue for $E_g$, green for $A_{1g}$, purple for $B_{1g}$ and orange for $B_{2g}$ modes. (c) Schematic of atomic motion (red arrows) associated to selected vibrational modes in TaTe$_{4}$ and NbTe$_{4}$, labeled according to the irreducible representation of the high-temperature groups at the $\Gamma$ high symmetry points. The low frequency $E_g$ mode displayed here is the one appearing at approximately 80.4 cm$^{-1}$ for TaTe$_4$ and 87.2 cm$^{-1}$ in the Raman data. The high frequency $E_g$ mode appears at 174.6 cm$^{-1}$ in TaTe$_{4}$ and at 213.8 cm$^{-1}$ in NbTe$_{4}$. The presented $A_{1g}$ mode appears at 136.0 (137.4) and 145.8 (144.3) cm $^{-1}$ for TaTe$_{4}$ (NbTe$_{4}$), while $B_{1g}$ and $B_{2g}$ modes appear at 125.5 (124.1) and 120.4 (120.9) cm$^{-1}$.
• Figure 3: (Color online) (a) Measured XRD patterns for the entire family of Ta$_{1-x}$Nb$_x$Te$_4$ crystals. The curve at the bottom of the upper panel corresponds to x = 0 (pure TaTe$_{4}$) and the one at the top corresponds to x = 1 (pure NbTe$_{4}$). The curves in between correspond to the doping series. The right panel shows a zoom-in to the (100) peaks. The lower panel shows the predicted XRD pattern for NbTe$_{4}$ (blue) and TaTe$_{4}$ (red), as calculated from the CIF file in the Materials Project website Horton2025. (b) Evolution of Raman peaks as a function of Nb doping rate $x$ across the solid solution Ta$_{1-x}$Nb$_{x}$Te$_{4}$. Here, the curve at the bottom corresponds to $x = 0$ (pure TaTe$_{4}$), the one at the top corresponds to $x = 1$ (pure NbTe$_{4}$), and intermediate compositions in between. The individual peaks for each $x$ value were fitted to individual Lorentzians, and presented in different colors according to the irrep assignment of Fig. 2(a,b). The black dashed curves correspond to the sum of the Lorentzian fits for each $x$, and the solid black lines correspond to the actual experimental data. The dashed vertical lines are used as visual guides to highlight the evolution of the different $E_g$ peaks.
• Figure 4: (Color online) : (a) Frequencies of the identified Raman peaks as a function of chalcogen doping. (b) Heatmaps showing the percentage variation of the different $E_g$ peaks as a function of doping level $x$, where $x=0$ for TaTe$_{4}$ and $x=1$ for NbTe$_{4}$. Here, the color indicates the intensity of the peak for each doping level. Blue represents peak absence, while intense red indicates doping levels where the intensity of the peak is the highest. The horizontal dashed lines are a visual guide to highlight the relative percentage evolution of the $E_g$ modes throughout the whole doping series.