First-order phase transition driven by competing charge-order fluctuations in 1T'-TaTe$_{2}$

TL;DR

This work tackles the microscopic origin of the first-order charge-density-wave transition in 1T'-TaTe$_2$ by combining x-ray diffraction, XPS, diffuse scattering, ARPES, IXS, and DFT with a two-order-parameter Ginzburg-Landau framework. It identifies a high-temperature incommensurate precursor at $q^*=(0, \frac{1}{4}+\delta, \frac{1}{2})$ competing with a low-temperature commensurate order at $q_\mathrm{CO}=(0, \frac{1}{3}, 0)$, with a dominant $q^*$ instability and a bond-driven $q_\mathrm{CO}$ channel. Diffuse scattering and ARPES link the $q^*$ precursor to nesting-driven electronic structure while DFT/IXS reveal an imaginary optical mode at $q^*$ and strong electron-phonon renormalization of a low-energy phonon; together they support a scenario where two order parameters couple ($\gamma\approx1$) to yield the first-order transition. The study provides a microscopic mechanism for discontinuous CDW transitions in quasi-1D and layered materials, highlighting competition between nesting-based and local-bonding-driven orders with potential relevance to other TMDs and related quantum materials.

Abstract

First-order phase transitions, characterized by a discontinuous change in the order parameter, are intriguing phenomena in condensed matter physics. However, the underlying, material-specific, microscopic mechanisms often remain unclear. Here, we unveil a high-temperature incommensurate charge-order precursor with the wave vector $\mathbf{q}^* = (0, \frac{1}{4}+δ, \frac{1}{2})$ in the 1T' phase of TaTe$_2$, which competes with fluctuating high-temperature Ta trimer bonding states at $\mathbf{q}_\mathrm{CO} =(0, \frac{1}{3}, 0)$. The precursor state follows the temperature dependence of the hidden incommensurability of the $\textit{quasi}$-1D nested Fermi surface. In contrast, the low-temperature commensurate charge order at $\mathbf{q}_\mathrm{CO}$, characterized by a charge disproportionation of the inequivalent Ta sites, appears to be driven by local chemical bonding. Dynamical lattice calculations identify an imaginary optical mode at $\mathbf{q}^*$, involving an in-plane vibration of the Ta atoms forming a chain-like structure that renormalizes below $T_\mathrm{CO}$. Our experimental and theoretical observations suggest that the controversial first-order phase transition, as captured by phenomenological Ginzburg-Landau theory, results from the competition between two order parameters: one involving Fermi surface nesting and the other involving local chemical bonding.

Figures (4)

• Figure 1: Structure, lattice parameters, and charge disproportionation of 1T'-TaTe$_2$. (A) Lattice structure of 1T'-TaTe$_2$. (B-C) High-temperature (HT) and low-temperature (LT) structures, which highlight the Ta atoms forming $(3\times1)$ zigzag chains and $(3\times3)$ butterfly-like structures, respectively. (D-E) Temperature dependence of the lattice parameters a, b, c, and the monoclinic bond angle $\beta$, showing a jump at the transition temperature of $\sim$180 K. (F) Core-level photoemission spectra of the spin-orbit split Ta 4f emissions in the HT phase (220 K) and LT phase (30 K). In the HT phase, the spectral contribution results from Ta$_1$ and Ta$_2$ sites that split up into A and B sites at low temperatures. Vertical gray bars indicate the energy window used to track the temperature-dependent Ta$_{1}^\mathrm{A}$ and Ta$_{1}^\mathrm{B}$ photoemission intensity. (G) Comparison of the temperature-dependent normalized resistance and the Ta$_{1}^\mathrm{A}$ and Ta$_{1}^\mathrm{B}$ 4f photoemission intensities.
• Figure 2: x-ray diffuse scattering of 1T'-TaTe$_2$. (A) Temperature dependence of the $(2H, K, H)$ diffuse maps, highlighting the diffuse signals at $\mathbf{q}_\mathrm{CO}=(0, \frac{1}{3}, 0)$ (red arrows in the 230 K panel) and $\mathbf{q}^*=(0, \frac{1}{4}+\delta, \frac{1}{2})$ (blue arrows) and the second harmonic of $\mathbf{q}^*$ (green arrows in the 178 K panel). (B) Temperature dependence of the diffuse scattering intensity in the $(0, K, L)$ plane. Dashed red and blue lines show the $K$ dependence of $\mathbf{q}_\mathrm{CO}$ and $\mathbf{q}^*$, respectively. (C) Temperature dependence of the diffuse scattering intensity and (D) correlation lengths ($\xi$) of $\mathbf{q}_\mathrm{CO}$ and $\mathbf{q}^*$. (E) Waterfall plot displaying the temperature dependence of the charge-order precursors in (A) and (B). (F) Temperature dependence of the incommensurability parameter $\Delta_\mathrm{incom} =q^*(T)-q^*(T_\mathrm{CO})$, as obtained from diffuse scattering, compared to the temperature dependence of the Fermi wavevector $k_{F_2}$. Also shown are corresponding results for quasi-1D K$_{0.3}$MoO$_3$.
• Figure 3: Angle-resolved photoemission spectroscopy of 1T'-TaTe$_2$. (A-B) Bulk and surface-projected Brillouin zones, as well as the high-symmetry directions of the undistorted $(1\times1)$ phase (black dashed hexagons), the HT $(3\times1)$ phase (red elongated hexagons), and the LT $(3\times3)$ phase (blue hexagons). The relevant $\Gamma^0$--$Z^1$ directions are indicated by the blue mini-Brillouin zones. (C) Experimental 3D Fermi surface at 20 K obtained using an incident photon energy of 65 eV. (D) $k_x$--$k_y$ projection of the experimental Fermi surface taken at 20 K ($h\nu=65$ eV), overlaid with the DFT-calculated Fermi surface. The red circles indicate the high-symmetry points of the HT $(3\times1)$ surface Brillouin zone, and the blue hexagon represents the LT $(3\times3)$ Brillouin zone. (E) Valence band (left panel)and linear dichroism (right panel) ($\mathrm{LD} = \mathrm{LH}-\mathrm{LV}$) ARPES spectra along the $\Gamma$--$Z$ symmetry direction at 20 K using 65 eV photons. Blue and red represent the spectral intensity obtained for linear horizontal (LH) and linear vertical (LV) polarized light, respectively. (F) Temperature-dependent evolution of the band spectrum crossing the Fermi level around the zone center along the $\Gamma^0$--$C$ symmetry direction.
• Figure 4: Inelastic x-ray scattering of 1T'-TaTe$_2$. (A) Unit cell of 1T'-TaTe$_2$ indicating Ta-atom vibrations at $\mathbf{q}^*$. (B) Theoretical harmonic phonon dispersion of the low-energy modes showing imaginary modes around $\mathbf{q}^*$ and $\mathbf{q}_\mathrm{CO}$. (C) Temperature dependence of the low-energy phonon modes $\omega_1$ and $\omega_2$ at $\mathbf{q}^*$. (D) Temperature dependence of $\nu_1$ and $\nu_2$ phonons at $\mathbf{q}_\mathrm{CO}$. (E) Wave-vector dependence of $\omega_1$ and $\nu_1$ at 250 K. Corresponding temperature dependence of (F) the integrated phonon intensity and (G) the energy and full width at half maximum (FWHM). (H) Temperature dependence of the competing order parameters associated with $\mathbf{q}_\mathrm{CO}$ and $\mathbf{q}^*$ according to a minimal Ginzburg--Landau model.