Bidirectional ultrafast control of charge density waves via phase competition

Abstract

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Leveraging time-resolved X-ray diffraction, we demonstrate ultrafast control of a CDW in EuTe$_4$ upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photo-excitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in EuTe$_4$, but also highlight the versatility of optical control over order parameters enabled by phase competition.

Figures (4)

• Figure 1: Phase competition and experimental setup. (a) Contour plots of equilibrium potential energy surfaces (PES) composed of two competing order parameters $\psi_1$ and $\psi_2$. The black circle marks the static global minimum. (b),(c) Contour plots of excited PES upon a moderate pump and an intense pump, respectively. The red circle marks the excited global minimum. (d) Schematic of the time-resolved X-ray diffraction (tr-XRD) setup with a near-infrared (NIR) pump centered at 800 nm. Eu and Te atoms are colored in purple and yellow, respectively. CDWs residing in the Te monolayers and bilayers are highlighted by blue and red waves, respectively, with their generated diffraction peaks labeled in the static reciprocal space mapping image of the (2 $K$$L$) plane.
• Figure 2: Temporal evolution of the $\mathbf{q_1}$ and $\mathbf{q_2}$ peak intensities $I$ normalized to their equilibrium values. Plots are taken with the pump fluence $F$ = 0.5 mJ/cm$^2$ and 0.3 mJ/cm$^2$, respectively, which are the lowest pump fluence employed in this work. Solid curves are fits to equations in \ref{['note1']}.
• Figure 3: Pump fluence ($F$) dependent CDW dynamics. (a),(b), Temporal evolution of the intensity $I$ acquired from the tr-XRD measurements normalized to their equilibrium values for selected $F$ of the $\mathbf{q_1}$ and $\mathbf{q_2}$ peaks, respectively. Solid curves are fits to equations in \ref{['note1']}. (c),(d), Temporal evolution of the normalized order parameter amplitude square $|\psi|^2$ obtained by TDGL simulations for selected $F$ of the CDW order parameters $\psi_1$ and $\psi_2$. Fluence ranges are identical for both order parameters. (e) Schematics of the decomposition of the $\mathbf{q_2}$ peak dynamics. The $\mathbf{q_2}$ peak dynamics can be considered as a summation of a photo-induced suppression and a phase-competition-induced enhancement that anticorrelates with the $\mathbf{q_1}$ peak suppression. Different fitting parameters defined in \ref{['note1']} are shown.
• Figure 4: (a) Pump fluence ($F$) dependence of the fitted magnitudes $A_1$ and $A_2$ of the $\mathbf{q_1}$ and $\mathbf{q_2}$ peaks. The sign of $A_1$ is flipped for direct comparison with $A_2$. (b) $F$ dependence of the fitted decay times $\tau_1$ and $\tau_2$ of the $\mathbf{q_1}$ and $\mathbf{q_2}$ peaks. Broad solid lines are guides to eyes. (c) $F$ dependence of the transient normalized intensity of the $\mathbf{q_2}$ peak at $t=1.1$ ps. Left inset shows the simulated fluence dependence of the CDW order amplitude square at a fixed time delay where the "peak" feature is maximal. Red and blue shadings highlight the light-enhanced and reduced regions, respectively, as pictorially shown by the right inset.