Nonlocal Probing of Amplitude Mode Dynamics in Charge-Density-Wave Phase of EuTe4

Amplitude mode is collective excitation emerging from frozen lattice distortions below the charge-density-wave(CDW)transition temperature TCDW and relates to the order parameter.Generally,the amplitude mode is non-polar(symmetry-even)and does not interact with incoming infrared photons.However,if the amplitude mode is polar(symmetry-odd),it can potentially couple with incoming photons,thus forming a coupled phonon-polariton quasiparticle that can travel with light-like speed beyond the optically excited region.Here,we present the amplitude mode dynamics far beyond the optically excited depth of ∼150 nm in the CDW phase of ∼10-μm-thick single-crystal EuTe4 using time-resolved x-ray diffraction.The observed oscillations of the CDW peak,triggered by photoexcitation,occur at the amplitude mode frequency ωAM.However,the underdamped oscillations and their propagation beyond the optically excited depth are at odds with the observation of the overdamped nature of the amplitude mode measured using meV-resolution inelastic x-ray scattering and polarized Raman scattering.The ωAM is found to decrease with increasing fluence owing to a rise in the sample temperature,which is independently confirmed using polarized Raman scattering and ab-initio molecular dynamics simulations.We rationalize the above observations by explicitly calculating two coupled quasiparticles—phonon-polariton and exciton-polariton.Our data and simulations cannot conclusively confirm or rule out the one but point toward the likely origin from propagating phonon-polariton.The observed non-local behavior of amplitude mode thus provides an opportunity to engineer material properties at a substantially faster time scale with optical pulses.

Four-dimensional imaging of lattice dynamics using ab-initio simulation

Time-resolved mapping of lattice dynamics in real-and momentum-space is essential to better understand several ubiquitous phenomena such as heat transport,displacive phase transition,thermal conductivity,and many more.In this regard,time-resolved diffraction and microscopy methods are employed to image the induced lattice dynamics within a pump–probe configuration.In this work,we demonstrate that inelastic scattering methods,with the aid of theoretical simulation,are competent to provide similar information as one could obtain from the time-resolved diffraction and imaging measurements.To illustrate the robustness of the proposed method,our simulated result of lattice dynamics in germanium is in excellent agreement with the time-resolved x-ray diffuse scattering measurement performed using x-ray free-electron laser.For a given inelastic scattering data in energy and momentum space,the proposed method is useful to image in-situ lattice dynamics under different environmental conditions of temperature,pressure,and magnetic field.Moreover,the technique will profoundly impact where time-resolved diffraction within the pump–probe setup is not feasible,for instance,in inelastic neutron scattering.