Ultrafast Decoherence of Charge Density Waves in K$_{0.3}$MoO$_{3}$

Recent works have suggested that transient suppression of a charge density wave (CDW) by an ultra-short excitation can lead to an inversion of the CDW phase. We experimentally investigate the dynamics of the CDW in K${0.3}$MoO${3}$ by time resolved x-ray diffraction after excitation with optical pulses. Our results indicate a transient inversion of the CDW phase close to the surface that evolves into a highly disordered state in less than one picosecond. Numerical simulations solving the Ginzburg-Landau equation including disorder from strong pinning defects reproduce our main observations. Our findings highlight the critical role of disorder in schemes for coherent control in condensed matter systems.

💡 Research Summary

In this work the authors investigate the ultrafast dynamics of the charge‑density‑wave (CDW) order in the quasi‑one‑dimensional compound K₀.₃MoO₃ using pump‑probe x‑ray diffraction at the SwissFEL free‑electron laser. A 30 fs, 510 nm optical pump is absorbed within ~190 nm of the surface, while a 7.5 keV, 50 fs x‑ray probe penetrates ~210 nm at a grazing incidence of 0.73°, ensuring that both pump and probe sample essentially the same depth profile. The (3 7.252 ‑2.5) super‑lattice reflection, which directly monitors the periodic lattice distortion (PLD) associated with the CDW, is recorded as a function of pump‑probe delay for several absorbed fluences ranging from 1.3 to 6.4 mJ cm⁻².

At the lowest fluence the diffraction intensity drops sharply within 0.2 ps, followed by coherent oscillations at ~1.7 THz (≈0.58 ps period). The oscillations decay within ~600 fs and the average intensity returns to its equilibrium value. As the fluence is increased, the oscillation amplitude diminishes, the average intensity remains suppressed, and at the two highest fluences a partial recovery appears at t₁ ≈ 0.33 ps. This recovery coincides with the first minimum of the low‑fluence oscillation and is interpreted as a transient inversion of the CDW phase: the order parameter Ψ passes through zero and overshoots, temporarily acquiring a π‑shifted phase.

Reciprocal‑space maps (RSMs) constructed at three selected delays (t₁ = 0.33 ps, t₂ = 0.68 ps, t₃ = 2.33 ps) reveal additional details. At low fluence the peak width Γ narrows slightly after excitation, whereas for fluences above 3 mJ cm⁻² the width broadens by ~10 % at t₁, indicating the formation of new domain walls associated with the phase‑inverted layer near the surface. At later times the width narrows again, but the momentum‑independent background offset ΔI₀ rises dramatically at t₃, suggesting that the CDW phase becomes spatially random, producing diffuse scattering.

To rationalize these observations the authors employ a time‑dependent Ginzburg‑Landau (GL) framework with a complex order parameter Ψ(𝐫,t). The free energy F_GL = a|Ψ|² + b|Ψ|⁴ + ξ²|∇Ψ|² captures the “sombrero” potential below the critical temperature T_c. The pump is modeled as a transient increase of the electronic temperature Tₑ(t,z) = T₀ + η Θ(t) e^{‑t/τ} e^{‑z/δ}. When η exceeds T_c − T₀, the coefficient a becomes positive near the surface, rendering Ψ = 0 the only stable point; the pre‑existing finite Ψ then oscillates around zero, producing the observed phase inversion.

Crucially, the model incorporates a random distribution of strong pinning defects. Each defect at position r_i favors a local phase φ_i, acting as a nucleation center for small CDW domains. The simulations are performed in three spatial dimensions, coupled to a two‑temperature model (electrons and a phononic heat bath), and the resulting Ψ(t,x,y,z) is used to compute synthetic diffraction patterns. The simulated intensity transients reproduce the suppression at high fluence, the transient peak recovery at t₁, the fluence‑dependent broadening of the RSM, and the large ΔI₀ increase at t₃. Depth‑resolved snapshots of |Ψ| and its phase show a clear π‑shift near the surface at t₁, followed by rapid dephasing around 0.8 ps and a highly disordered configuration thereafter.

The authors note that a simple GL model with only a time‑dependent a‑parameter would predict a softening of the oscillation frequency at high fluence, which is not observed experimentally. By introducing two coupled order parameters (electronic and lattice) they recover the experimentally observed lack of softening, consistent with previous work showing that the electronic subsystem cannot adiabatically follow the lattice motion under strong excitation.

From these results the authors conclude that disorder, in the form of strong pinning defects, is the dominant mechanism for the ultrafast decoherence of the CDW after a transient phase inversion. The defects cause rapid spatial randomization of the CDW phase, destroying long‑range coherence within less than a picosecond. This insight clarifies why previous phenomenological models that employed a time‑dependent damping constant could fit the data but lacked a microscopic basis. Moreover, the observation that a second pump pulse can keep the system in the high‑symmetry single‑well potential for a longer interval suggests a route to extend coherent oscillations by temporally shaping the excitation.

Overall, the study demonstrates that any attempt at coherent control of collective electronic orders must explicitly consider the role of intrinsic disorder. In CDW systems, and likely in other symmetry‑broken phases such as superconductors or spin‑density‑waves, pinning defects set a fundamental limit on how long a laser‑induced coherent state can survive. The combination of ultrafast x‑ray diffraction with realistic three‑dimensional GL simulations provides a powerful methodology for dissecting these limits and for guiding the design of materials where disorder is either minimized or engineered to achieve desired dynamical functionalities.