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

TL;DR

The paper investigates room-temperature CDW fluctuations in TiSe2 using time-resolved XUV momentum microscopy and first-principles theory. It demonstrates ultrafast melting and recovery of CDW fluctuations, including a coherent amplitude phonon mode that persists above Tc, and shows that dynamical electron-phonon coupling—rather than purely excitonic effects—dominates the fluctuations. Theoretical analysis with Fan-Migdal self-energy and DFPT-based inputs reproduces key spectral features, such as backfolded Se 4p replicas and M-point phonon dynamics, linking the fluctuation behavior to a soft phonon that hardens with temperature. The results clarify the microscopic origin of CDW fluctuations and suggest that electron-phonon interactions play a central role in both room-temperature fluctuations and low-temperature CDW formation, with implications for other TMDCs and related correlated systems.

Abstract

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.

Figures (4)

• Figure 1: Experimental and theoretical methodologies for investigating CDW fluctuations in 1T-TiSe$_2$.(a) Polarization-tunable infrared pump (1030 nm, 135 fs, 0.95 mJ/cm$^2$) and XUV probe pulses (21.6 eV) are focused at an incidence angle of 65$^{\circ}$ on a 1T-TiSe$_2$ sample at room temperature (295 K) in the interaction chamber of a time-of-flight momentum microscope, capable of collecting photoelectrons from the entire 2$\pi$ solid angle in an energy range of several eV. (b) Three-dimensional photoemission intensity $I(E_\mathrm{B}, k_x, k_y)$ and associated energy-momentum cut along M-$\Gamma$-M' and K-$\Gamma$-K', acquired using s-polarized IR pump pulse (1.2 eV, 135 fs, $\sim$0.95 mJ/cm$^2$) and while continuously rotating the linear polarization axis angle of the XUV probe beam (21.6 eV) at the pump-probe temporal overlap. The photoemission intensity is integrated for all XUV polarization axis angles. (c) Comparison between experimental and theoretical constant energy contours (CECs), near the Fermi level. The measured loss of spectral weight within M pockets (black arrows) is well captured by theoretical calculations, which include dynamical electron-phonon interaction for temperatures above the CDW transition temperature $T_{\rm CDW}$.
• Figure 2: Equilibrium and excited state band structure in 1T-TiSe$_2$ at Room Temperature The first row (a,b) presents the static band structure before IR pump excitation. In contrast, the second row (c,d) describes the excited band structure at the pump-probe pulse time overlap at time zero. (a, c) Energy-momentum cut along the M-$\Gamma$-M' direction before and at the excitation by the pump pulse. The intensity is integrated for continuously varied linear polarization between horizontal and vertical. Dashed markers indicate where the momentum distribution curves (MDCs) in (b, d) were extracted. The lines in (b, d) indicate the position of Se 4p replica, and (a,c) are overlaid with a sketch of the normal phase band structure.
• Figure 3: Ultrafast melting and recovery of RT-CDW fluctuations in 1T-TiSe$_2$(a)-(b) Differential constant energy contour (integrated over -23 meV$< \mathrm{E-E_F} <$12 meV) and energy-momentum cut near the M pocket, obtained by subtracting photoemission intensity before (integration between -880 fs and -720 fs) and during pump-probe temporal overlap (integration between -80 fs and 80 fs). (c) Time-dependent photoemission intensity for different regions of interest (ROIs) along with corresponding fits. Purple dots represent the IR/XUV cross-correlation extracted from the time-dependent laser-assisted photoemission signal (ROI not shown), with an FWHM duration of 171 fs (Gaussian fit, purple line). Red, black, and blue dots denote time-resolved photoemission intensity from the respective ROIs shown in (b), while the associated lines indicate fits. (d) Blue dots and dashed line represent the residual intensity obtained by subtracting the double exponential fit from the photoemission intensity in the blue ROI in (b) (CDW backfolded band), while the thick blue line represents the Fourier filtered data (bandpass filter around 3.52 THz) indicating coherent oscillation of the CDW amplitude mode. (e) The electronic temperature as a function of pump-probe delay (orange) extracted by Fermi-Dirac distribution fitting, alongside with the backfolded band intensity (blue) and the excited state population dynamics (yellow).
• Figure 4: Signatures of CDW fluctuations from dynamical electron-phonon scattering.(a) Electron spectral function of 1T-TiSe$_2$ along $\Gamma$-M high symmetry direction with dynamical electron-phonon interaction included for temperature just above the CDW transition temperature $T_{\rm CDW}$. (b) The corresponding constant energy contour, where black arrows show the loss of spectral weight within the M pocket. (c)-(d) Same as (a)-(b) but close the temperature $T^{\ast}$, i.e. when CDW fluctuations are diminished. Red lines represent the bare bands without dynamical electron-phonon coupling included. (e) MDC cuts for several temperatures above the $T_{\rm CDW}$ for energy well below the Ti-3d conduction band [see dashed line in panels (a) and (b)]. (f) Phonon spectral function along the $\Gamma$-M-K-$\Gamma$ high-symmetry path, with dynamical electron-phonon coupling included. The temperature is 50 K above $T_{\rm CDW}$. The red curve shows the phonon dispersions without including spectral broadening due to electron-phonon scattering. The right panel shows the phonon energy at the M point (orange dashed line).