Tracking the Catastrophic Collapse of Hybrid Exciton-Phonon Order in a Quantum Material

Abstract

Revealing the interactions binding electronic and lattice components of cooperative quantum order is central to sculpting new states of matter. This challenge is epitomized by the charge density wave material 1T-TiSe$_2$, where photoexcitation disrupts its presumed hybrid exciton-phonon order. This exposes a paradox: the electronic component collapses within femtoseconds while the periodic lattice distortion persists. If the lattice distortion outlives the excitonic condensate, were they truly intertwined? Here we resolve this by uncovering a low-frequency mode (approx. 0.13 THz) emerging only in the ordered state, signaling exciton-phonon coupling. This mode is consistent with a locked phason -- a collective excitation arising if coupling between the excitonic condensate and lattice reduces continuous phase symmetry to a discrete one, giving the excitonic Goldstone mode finite mass. This is captured by an effective theory describing a shared potential landscape. At a critical threshold, the collapse of excitonic order flattens the potential, triggering an exciton-phonon catastrophe: selective overheating of the charge density wave phonon, disappearance of the locked phason, and sudden loss of electronic coherence. Remarkably, the lattice distortion survives as a dynamically trapped, non-thermal remnant, confirmed by the anomalous temperature dependence of the phononic response. These findings demonstrate that coupled potential energy landscapes can be manipulated to selectively dismantle complex quantum orders, advancing material control through dynamical design.

Figures (8)

• Figure 1: Raman access to coupled order in 1T-TiSe$_2$.a, Schematic free-energy landscape of the complex order parameter $\Delta = |\Delta| e^{i\varphi}$. Left: in the absence of locking, the potential has a Mexican-hat shape with a degenerate circle of minima in the $(\mathrm{Re}\,(\Delta), \mathrm{Im}\,(\Delta))$ plane, and the phason corresponds to motion along the phase coordinate $\varphi$. Right: pinning to an external potential, e.g., exciton-phonon interactions, lifts this degeneracy, thereby turning the phason into a locked finite-frequency mode. b, Overview of the experimental configuration and processes. Time-resolved Raman spectroscopy setup combining a femtosecond 750 nm pump with a time-delayed 513 nm probe in parallel backscattering geometry. Inset: Pump-probe Raman process; the pump pulse excites electrons, which relax by emitting phonons; the delayed probe detects Stokes (phonon creation) and anti-Stokes (phonon annihilation) photons. c, Temperature-dependent Raman spectra under weak CW excitation at 532 nm. Below $T_\mathrm{CDW} \approx 202$ K, folded $A_{1g}^*$ and $E_g^*$ modes appear. d, Evolution of phonon energies. The $A_{1g}^*$ mode hardens upon cooling, with $A_{1g}^*$ near 116 cm$^{-1}$ at low temperature, serving as the primary phononic marker of the CDW. e, Schematic phonon dispersions from DFT in the normal phase (NP, top) and in the CDW phase (CDW, bottom), showing only the branches relevant for the discussion. In the NP, the $A_{\mathrm{1g}}$ branch (red) is Raman active at $\Gamma$, while the soft $M_2$ branch (blue) resides at the zone-boundary M point and is therefore not accessible in first-order Raman scattering. In the CDW phase, Brillouin-zone folding maps M onto the new zone centre $\Gamma'$, where the former $M_2$ branch appears as the folded $A_{\mathrm{1g}}^{\mathrm{*}}$ mode (blue). The emergence of $A_{\mathrm{1g}}^{\mathrm{*}}$ at $\Gamma'$ in the Raman spectra is thus a direct fingerprint of the PLD.
• Figure 1: Phonon dispersion of 1T-TiSe$_2$. (a) Phonon dispersion in the normal phase (space group $P\bar{3}m1$) from DFT simulations. (b) Phonon dispersion in the CDW phase (space group $P\bar{3}c1$). The $A_{1g}^{*}$ and $E_{g}^{*}$ modes originate from M (or L)-point phonons that fold to the new $\Gamma'$ point in the reduced Brillouin zone, consistent with the zone-folding picture of the CDW. (c) Unfolded phonon dispersion of the CDW phase of TiSe$_2$. The false-colour scale (arbitrary units), indicated by the colour bar on the right, shows the weights of the projections of the CDW phonon branches onto the irreducible representations of the little groups of the 3-atom primitive structure. The $k$-point labels refer to the unfolded (primitive) Brillouin zone, from $\Gamma$ to $M$. The phonon unfolding was performed using the UPHO code PhysRevB.95.024305.
• Figure 2: Critical transformation of the CDW phonon under photoexcitation.a--c, Time-resolved Raman maps of the pump-induced differential intensity $\Delta I(t,\omega)$ under three representative conditions. a, High fluence at 295 K: $\Delta I$ shows a strong low-energy Raman continuum (LERC) and population of the normal-phase $A_{\mathrm{1g}}$ near 200 cm$^{-1}$. b, Low fluence at 5 K: $\Delta I$ contains LERC and the folded CDW phonon $\Delta I_{A_{1g}^{*}}$. c, High fluence at 5 K: the LERC and $\Delta I_{A_{1g}}$ dominate the spectrum, and $\Delta I_{A_{1g}^{*}}$ becomes spectrally obscured by the LERC. d, Differential spectra $\Delta I(\omega)$ at a fixed delay of 1.75 ps for fluences as indicated. $\Delta I_{A_{1g}^{*}}$ (blue) dominates at low fluence, weakens near the threshold $F_c \approx 187~\mu$J cm$^{-2}$, and the normal-phase $\Delta I_{A_{1g}}$ (red) emerges abruptly above threshold, while the broadband $\Delta I_{\mathrm{LERC}}$ increases steadily. e, Time trace of the CDW mode $\Delta I_{A_{1g}^{*}}$ at 46 $\mu$J cm$^{-2}$ and 5 K, showing that the slowly slowly decaying dynamics are modulated by a $\sim$7.5 ps (0.13 THz) oscillation (arrows), revealing the locked phason coupled to $A_{\mathrm{1g}}^{\mathrm{*}}$. f, Dynamics of $A_{\mathrm{1g}}^{\mathrm{*}}$ for fluences as indicated, the oscillation amplitude decreases while its period increases, indicating locked phason softening (see diamonds). g, Fluence dependence of the extracted intensities: $\Delta I_{\mathrm{LERC}}$ grows superlinearly ($\propto F^{1.51\pm0.08}$); $\Delta I_{A_{1g}}$ appears only above $F_c$ and shows extreme nonlinearity ($\propto F^{6.99\pm0.40}$); the amplitude of $\Delta I_{A_{1g}^{*}}$ initially scales linearly with fluence ($\propto F^{1.00 \pm 0.10}$), but saturates as $F \geq F_c$. h, The locked phason amplitude grows only within a narrow low-fluence range and vanishes near $F_c$, revealing a distinct behavior that identifies it as a separate collective excitation.
• Figure 2: Fluence-dependent behavior of the hybrid exciton-phonon mode.a-c, Residual coherent oscillations of the photoinduced $A_{1g}^*$ phonon dynamics after exponential background subtraction (Supplementary Note 6) for three representative fluences. Extracted amplitude (d), damping time (e), and period (f) as a function of excitation fluence. At low fluence, the oscillations are long-lived and periodic; with increasing fluence, the hybrid mode softens and damps, disappearing above $100~\mu\mathrm{J\,cm}^{-2}$. This behavior indicates a fluence-driven collapse of the hybrid locked phason mode.
• Figure 3: Selective overheating and saturation of the CDW phonon.a, Time-resolved anti-Stokes (AS) and Stokes (S) Raman spectra at selected delays for increasing fluences. At $F = 139~\mu$J cm$^{-2}$, the anti-Stokes and Stokes amplitudes of the $A_{\mathrm{1g}}^{\mathrm{*}}$ mode become nearly equal (dashed box), $I_\mathrm{AS} \approx I_\mathrm{S}$, indicating a strongly overheated, highly populated $A_{\mathrm{1g}}^{\mathrm{*}}$ phonon. Above $F_c$, the $A_{\mathrm{1g}}^{\mathrm{*}}$ response saturates and an AS-active contribution from the normal-phase $A_{\mathrm{1g}}$ mode emerges. b, Delay-dependent intensity $\Delta I_{A_{1g}^{*}}$ of anti-Stokes and Stokes signals from theory (top) and experiment (bottom) at $F = 18~\mu$J cm$^{-2}$. c, Fluence dependence of the anti-Stokes spectra at t = 2 ps. The $A_{\mathrm{1g}}^{\mathrm{*}}$ mode persists over all fluences, while $A_{\mathrm{1g}}$ emerging above $F_c$. d, Fluence-dependent time-resolved reflectivity (TRR) dynamics, dominated by $A_{\mathrm{1g}}^{\mathrm{*}}$ oscillations. Oscillations persist at all fluences, but become rapidly damped as $F$ approaches $F_c$. The dynamics are normalized to the initial transient reflectivity change, which increases with fluence, making the coherent $A_{\mathrm{1g}}^{\mathrm{*}}$ oscillations appear reduced, although their absolute amplitude increases and eventually saturates (Supplementary Note 11). e, Anti-Stokes fits of $A_{\mathrm{1g}}^{\mathrm{*}}$ peak parameters versus fluence. Top: phonon frequency shows softening; bottom: amplitude saturates above $F_c$. f, TRR analysis of $A_{\mathrm{1g}}^{\mathrm{*}}$: both oscillation frequency and amplitude saturate near $F_c$, consistent with Raman results. g, Theoretical model reproduces the saturation behavior of the $A_{\mathrm{1g}}^{\mathrm{*}}$ amplitude observed in the experiment.