Ultrafast Stiffening of the Lattice Potential and Metastable State Formation in 1$T$-TiSe$_2$

Abstract

We use ultrafast optical spectroscopy to investigate the electronic and lattice dynamics of the charge-density wave (CDW) material 1$T$-TiSe$_2$ across various temperatures and pump fluences. We reveal a close relationship between the observed ultrafast dynamical processes and two characteristic temperatures: $T_{\rm CDW}$ ($\sim$202 K) and $T^*$ ($\sim$165 K). Two coherent phonon modes are identified: a high-frequency $A_{1g}$ mode ($ω_{1}$) and a lower-frequency $A_{1g}$ CDW amplitude mode ($ω_{2}$). In stark contrast to thermal melting, where phonons soften, the CDW amplitude mode exhibits anomalous hardening (frequency upshift) with increasing pump fluence. We establish this hardening as the direct signature of an ultrafast restoration of the bare lattice potential. The photoexcited carrier plasma screens the long-range electron-phonon interactions that drive the Peierls-like instability, effectively ``undressing" the soft phonon and driving its frequency toward the stiffer value of the unrenormalized lattice. Furthermore, an abrupt increase in the excited state buildup time above a critical pump fluence marks a sharp boundary to a photoinduced metastable metallic state. These findings demonstrate that the CDW order in 1$T$-TiSe$_2$ is governed by a fragile, fluence-tunable competition between excitonic correlations and lattice dynamics.

Figures (4)

• Figure 1: (a) Electronic structure of 1$T$-TiSe$_2$ along $\Gamma$-M in the normal state ($T > T_{\rm CDW}$). (b) Band structure near M/$\Gamma^*$ in the CDW state ($T < T_{\rm CDW}$), illustrating band folding and the subsequent hybridization between the folded Se 4$p$ and Ti 3$d$ bands, leading to the formation of excitonic correlations between electron-hole pairs.
• Figure 2: Temperature-dependent ultrafast reflectivity dynamics of 1$T$-TiSe$_2$. (a) Transient $\Delta R/R$ vs. delay time over temperatures ranging from 10 to 300 K at a pump fluence of $\sim$40 $\mu$J/cm$^2$. Note the break in the $x$ axis. (b) 2D pseudocolor map of $\Delta R/R$ as a function of delay time and temperature. (c) Bi-exponential fits (blue lines) to $\Delta R/R$ at selected temperatures. Arrows indicate the initial ($\tau_1$) and second ($\tau_2$) relaxation processes. (d1, d2) Amplitude ($|A_1|$) and lifetime ($\tau_1$) of the initial relaxation as a function of temperature. (e1, e2) Amplitude ($A_2$) and lifetime ($\tau_2$) of the second relaxation as a function of temperature. (f) Temperature dependence of buildup time ($\tau_{Buildup}$) as defined in (a). The vertical blue and green dashed lines indicate $T_{\rm CDW}$ and $T^*$, respectively.
• Figure 3: Oscillatory part of temperature-dependent data (a) Oscillations from the transient reflectivity at five selected temperatures, with blue lines represent fits using Eq. (1). (b) False-color FFT spectrum as a function of frequency and temperature. (c) Temperature dependence of $\omega_1/2\pi$ and $\omega_2/2\pi$ from the FFT (squares) and fits (circles). The solid magenta lines is a fit to the frequency $\omega_2$ with a mean-field-like as described in the text. (d) Temperature dependence of damping rates $\Gamma_1$ and $\Gamma_2$ from fits. The solid cyan lines in (c) and (d) are anharmonic phonon model fit to data obtained from fitting to Eq. (1). (e) Temperature dependence of FFT amplitudes of $\omega_1$ and $\omega_2$.
• Figure 4: Pump fluence-dependent ultrafast dynamics of 1$T$-TiSe$_2$. (a) Transient $\Delta R/R$ as a function of delay time for various pump fluences at 4 K. (b) 2D pseudocolor map of $\Delta R/R$ as a function of delay time and pump fluence. (c) False-color FFT spectrum as a function of frequency and pump fluence. (d1,d2) Fluence dependence of $\omega_1$ frequency and FFT amplitude at different temperatures. (e1, e2) Fluence dependence of $\omega_2$ frequency and FFT amplitude at different temperatures. (f) Fluence dependence of $\tau_{Buildup}$ for various temperatures. (g) Temperature dependence of critical fluence $F_c$. The dashed black line is a fit to the $F_c(T)$ using an empirical mean-field expression for a second-order phase transition, $F_c(T) \propto$ tanh$^2[\alpha \sqrt{T_{\rm CDW}/T - 1}\Theta(T_{\rm CDW}-T)]$ZTLiu2023, where $\alpha$ is a fitting parameter and $\Theta$ is the Heaviside step function.