Electron-phonon-dominated charge-density-wave fluctuations in TiSe$_2$ accessed by ultrafast nonequilibrium dynamics

The complex phase diagram of 1T-TiSe2 consists of a charge density wave (CDW) below 200 K, and CDW fluctuations of still unknown origin at higher temperatures. Here, we use time-resolved extreme ultraviolet momentum microscopy and density functional perturbation theory to uncover the formation mechanism of CDW fluctuations and their spectral features at 295 K. We investigated the transient dynamics of fluctuations upon nonresonant ultrafast photoexcitation, and directly correlate it with the CDW soft-phonon hardening. Surprisingly, our results show that the coherent amplitude mode modulating ultrafast CDW recovery persists above TCDW, and reveal that CDW fluctuations are dominated by the electron-phonon interaction rather than excitonic correlations as commonly believed. Our findings on these microscopic CDW fluctuations clarify the complex interplay between electronic and lattice degrees of freedom at elevated temperatures and, therefore, could be useful in understanding the nature of the CDW phase transition in 1T-TiSe2 and similar quantum materials.

💡 Research Summary

The authors investigate the origin of charge‑density‑wave (CDW) fluctuations in 1T‑TiSe₂ at temperatures well above the CDW transition (T_CDW ≈ 200 K), focusing on the room‑temperature regime (295 K). Using a state‑of‑the‑art time‑resolved extreme‑ultraviolet (XUV) momentum microscope combined with a polarization‑tunable infrared pump (1030 nm, 135 fs, ≈0.95 mJ cm⁻²), they acquire three‑dimensional photo‑emission intensity I(E_B, k_x, k_y) over the full Brillouin zone and track its evolution as a function of pump‑probe delay (Δt). By continuously rotating the XUV linear polarization and summing over all angles, matrix‑element effects are minimized, allowing a clear view of the back‑folded Se 4p band that serves as the hallmark of CDW order.

Static measurements at 295 K reveal a faint but distinct back‑folded Se 4p replica at the M(L) points, confirming the presence of CDW fluctuations even in the normal phase. Density‑functional perturbation theory (DFPT) calculations that include temperature‑dependent electron‑phonon coupling reproduce the loss of spectral weight observed experimentally, indicating that a strongly coupled soft phonon remains relevant above T_CDW.

Upon photoexcitation, the authors observe an ultrafast melting of the CDW‑related spectral weight within the temporal resolution of the experiment (≈170 fs). The melted signal recovers on a sub‑picosecond timescale (τ ≈ 700 fs). Importantly, the recovery is not a simple exponential; after subtracting the monotonic component, a residual oscillation at ≈3.5 THz (≈23 meV) is uncovered. This frequency matches the A₁g CDW amplitude phonon previously identified in the ordered phase, demonstrating that the coherent amplitude mode survives in the fluctuation regime and modulates the recovery dynamics.

The DFPT analysis shows that the same soft phonon, which is strongly hybridized with the Se 4p states at equilibrium, hardens (increases in frequency) when the electronic distribution is transiently heated by the pump. This hardening weakens the electron‑phonon interaction momentarily, providing a natural explanation for the observed melting of the back‑folded band. In contrast, excitonic correlations are predicted to be quenched already above T_CDW and to disappear at pump fluences far lower than those used here. The persistence of the back‑folded band at high fluence therefore argues against a purely excitonic origin of the fluctuations.

Overall, the study presents several key insights: (i) CDW fluctuations at room temperature are dominated by electron‑phonon coupling rather than excitonic effects; (ii) the CDW amplitude phonon remains coherent above T_CDW and directly influences the nonequilibrium dynamics of the fluctuating order; (iii) ultrafast melting and recovery of the fluctuating CDW occur on distinct timescales that can be disentangled by momentum‑resolved spectroscopy; (iv) the combination of XUV momentum microscopy with first‑principles electron‑phonon calculations provides a powerful platform for probing hidden orders in quantum materials.

These findings not only resolve a long‑standing debate on the driving mechanism of CDW fluctuations in TiSe₂ but also have broader implications for related phenomena such as unconventional superconductivity, chiral CDW states, and light‑induced hidden phases in transition‑metal dichalcogenides and other strongly correlated systems.