CDW Gap Collapse and Weyl State Restoration in (TaSe4)2I via Coherent Phonons: A First-Principles Study

TL;DR

The paper tackles nonthermal control of topology in the CDW material (TaSe4)2I by identifying symmetry-preserving phonon modes that collapse the direct electronic gap along the Gamma-Z path and yield Weyl nodes. Using first-principles phonon analysis, it finds nine Raman-active A modes capable of inducing a CDW-to-Weyl transition, with the A(18) mode at 2.51 THz being the most efficient driver, capable of reducing the minimum direct gap to the meV scale at moderate distortions and producing Weyl nodes at generic k-points. The study also uncovers strong anharmonic coupling between A(18) and the low-frequency IR mode B3(7), described by terms c_{21} Q_IR^2 Q_R and d_{22} Q_IR^2 Q_R^2, which enables an indirect, nonthermal route to activate the Raman mode and reach the Weyl regime. Collectively, these findings offer a predictive, lattice-based framework for ultrafast topological switching in quasi-one-dimensional CDW materials and guide experimental THz pump–probe strategies for realizing and probing Weyl semimetal phases.

Abstract

Coherent phonon excitation offers a nonthermal route to control quantum phases of condensed matter. In this work, we employ first-principles calculations to investigate the phonon landscape of (TaSe4)2I in its charge-density-wave (CDW) phase. We identify nine symmetry-preserving Raman-active modes that can suppress the Gamma-Z direct gap to the meV scale and render the system globally gapless by generating Weyl nodes at generic k points. Among them, the 2.51 THz CDW amplitude mode A(18) directly weakens the Ta-chain tetramerization, approaching a transient restoration of the uniform-chain geometry. It is also the most efficient mode owing to its low frequency and a relatively small critical displacement dominated by Ta motions. Other Raman modes, dominated by Se vibrations, require significantly larger displacements to reach the Weyl-semimetallic regime and are generally less effective than A(18) at reducing the Ta-chain tetramerization. Furthermore, we explore nonlinear phonon-phonon interactions and find that the low-frequency infrared-active mode B3(7) (1.14 THz) exhibits strong anharmonic coupling with A(18), providing an indirect pathway to drive the system toward a Weyl-semimetallic regime. Our results provide predictive insight for ultrafast pump-probe experiments and present a generalizable framework for lattice-driven topological switching in quasi-one-dimensional quantum materials.

Figures (7)

• Figure 1: (a) Top view and (b) side view of the conventional cell of (TaSe$_4$)$_2$I in the CDW phase. Blue arrows indicate the eigenvectors of the 2.51 THz Raman-active mode $A(18)$, which preserves the $F222$ symmetry. (c) Schematic of Ta-chain tetramerization in three configurations: the non-CDW state (left), the CDW state (middle), and the CDW state distorted along the $A(18)$ eigenvector (right). Green stars mark the centers of the long Ta--Ta separations on the two chains: Ta$_\mathrm{I}$(1)--Ta$_\mathrm{I}$(3) on chain I (labeled at Ta$_\mathrm{I}$(2)) and Ta$_\mathrm{II}$(3)--Ta$_\mathrm{II}$(1$^\prime$) on chain II (labeled at Ta$_\mathrm{II}$(4)). Red stars mark the centers of the short Ta--Ta separations: Ta$_\mathrm{II}$(1)--Ta$_\mathrm{II}$(3) on chain II (labeled at Ta$_\mathrm{II}$(2)) and Ta$_\mathrm{I}$(3)--Ta$_\mathrm{I}$(1$^\prime$) on chain I (labeled at Ta$_\mathrm{I}$(4)). Here Ta$_\mathrm{I}$(1$^\prime$) and Ta$_\mathrm{II}$(1$^\prime$) denote the periodic images in the neighboring unit cell. Blue arrows illustrate the $A(18)$-induced displacement pattern.
• Figure 2: (a) Phonon displacement-dependent band gap along $\Gamma\text{--}\mathrm{Z}$ in the CDW phase. Three red circles mark the $A(18)$ normal-mode amplitudes $Q$ (in $\text{\AA}\sqrt{\mathrm{amu}}$) corresponding to the band structures shown in panels (b) (c) and (d). (b) Electronic band structure along the high-symmetry path $\Gamma\text{--}\mathrm{Z}$ at equilibrium ($Q = 0$), showing a band gap of 0.32 eV. (c) Electronic band structure at $Q = 2.0$, where the Ta--Ta bond disproportionation (the long and short Ta--Ta distances become equal), indicating a transient restoration of the uniform-chain geometry (CDW melting in the structural sense); the $\Gamma\text{--}\mathrm{Z}$ gap is reduced to $5.8$ meV. (d) Electronic band structure at $Q = 2.5$, where where the minimum direct gap along $\Gamma\text{--}\mathrm{Z}$ is reduced to $3.0$ meV. The inset magnifies the energy window $E-E_F\in[-0.06,0]$ eV to resolve the residual gap. (e) Weyl nodes obtained from a Brillouin-zone--wide search for the phonon-modulated structure at $Q=2.0$, projected onto the $k_x$--$k_y$ plane (left) and the $k_{\parallel}$--$k_z$ plane (right). (f) Same as (e) but for $Q=2.5$. Red and blue spheres denote Weyl nodes with positive and negative chirality, respectively; all nodes shown lie within 10 meV of the Fermi level. Here $k_{\parallel}=(k_x+k_y)/\sqrt{2}$ is the in-plane momentum along the $[110]$ direction, plotted in units of $2\pi/a_{\parallel}$ with $a_{\parallel}=\sqrt{a^2+b^2}$.
• Figure 3: Phonon-driven $\Gamma\text{--}\mathrm{Z}$ gap suppression in (TaSe$_4$)$_2$I by Raman-active modes beyond the CDW amplitude mode. (a–h) Results for eight representative Raman-active modes: $A(30)$, $A(33)$, $A(40)$, $A(41)$, $A(44)$, $A(47)$, $A(50)$, and $A(62)$, respectively. For each mode, the first and second panels show the phonon eigenvectors in the top and side views, respectively; blue arrows indicate the atomic displacement directions, with dominant motion observed on Se atoms. The third panels show the evolution of the band gap along the $\Gamma\text{--}\mathrm{Z}$ path as a function of the normal mode coordinate $Q$, showing that each mode can suppress the gap to the meV scale at a mode-dependent near-closure amplitude $Q_\mathrm{c}$ (Table \ref{['Table1']}). The fourth panels present corresponding electronic band structures along $\Gamma\text{--}\mathrm{Z}$ at $Q=Q_\mathrm{c}$, showing a near-touching along $\Gamma\text{--}\mathrm{Z}$ with a meV-scale residual gap. Insets zoom into the near-$E_F$ energy range to resolve the meV-scale residual opening; the energy window is chosen individually for each mode for clarity. The fifth panels show Brillouin-zone--wide Weyl-node searches for the phonon-distorted structures at $Q=Q_\mathrm{c}$, showing that the Weyl nodes occur at generic $k$ points rather than exactly on the $\Gamma\text{--}\mathrm{Z}$ line.
• Figure 4: Nonlinear coupling between the IR-active mode $B_3(7)$ and the CDW amplitude mode $A(18)$. (a) and (b) show the top and side views of the atomic displacements (eigenvectors) for the $B_3(7)$ mode, respectively, highlighting Ta atom vibrations along the c-axis, similar to the $A(18)$ mode. (c) Anharmonic potential energy surface of the Raman $A(18)$ mode modulated by the $B_3(7)$ IR mode. The three curves correspond to three different amplitudes of the $B_3(7)$ mode: the black dashed line represents $Q_{B_3(7)} = 0.0$, showing the baseline potential energy curve of $A(18)$ in the absence of IR distortion; the orange dashed line corresponds to $Q_{B_3(7)} = \pm 1.0$, where the energy landscape slightly stiffens; and the blue dashed line corresponds to $Q_{B_3(7)} = \pm 2.0$, showing a noticeable increase in curvature, indicating enhanced anharmonicity and stiffer restoring forces for $A(18)$. (d) Schematic comparison between the $B_3(7)$ and $A(18)$ modes, demonstrating the additional two-fold symmetry breaking caused by $B_3(7)$ mode displacement.
• Figure A1: Direct-gap response on different high-symmetry paths under frozen-phonon distortions in the $F222$ CDW phase of $(\mathrm{TaSe}_4)_2\mathrm{I}$. (a) Brillouin zone and the high-symmetry points used in this section. (b) Electronic band structure at equilibrium ($Q=0$) along the selected high-symmetry paths; the colored segments highlight the three paths used for direct-gap tracking: $\Gamma\text{--}\mathrm{Z}$ (yellow), $\mathrm{X}\text{--}\mathrm{G}_{0}\!\mid\!\mathrm{H}_{0}\text{--}\mathrm{Y}$ (blue), and $\Gamma\text{--}\mathrm{L}$ (green). (c)--(k) Minimum direct band gap as a function of the normal-mode amplitude $Q$ for representative Raman-active $A$ modes, comparing the three paths on the same energy scale and with identical electronic-structure settings as in the main text.