Time- and momentum-resolved phonon population dynamics with ultrafast electron diffuse scattering

Abstract

Interactions between the lattice and charge carriers can drive the formation of phases and ordering phenomena that give rise to conventional superconductivity, insulator-to-metal transitions, and charge-density waves. These couplings also play a determining role in properties that include electric and thermal conductivity. Ultrafast electron diffuse scattering (UEDS) has recently become a viable laboratory-scale tool to track energy flow into and within the lattice system across the entire Brillouin zone, and to deconvolve interactions in the time domain. Here, we present a detailed quantitative framework for the interpretation of UEDS signals, ultimately extracting the phonon mode occupancies across the entire Brillouin zone. These transient populations are then used to extract momentum-and mode-dependent electron-phonon and phonon-phonon coupling constants. Results of this analysis are presented for graphite, which provides complete information on the phonon-branch occupations and a determination of the A 1 phonon mode-projected electronphonon coupling strength g 2 e,A 1 = 0.035 ± 0.001 eV 2 that is in agreement with other measurement techniques and simulations.

Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft phonons in TiSe 2

“…However, the frequency of phonons along the soft M-L transverse branch is only in the 1-to 2-THz (4-to 8-meV) range and is more highly populated than all other zone-boundary modes, which are about two times higher in frequency (13,40). This distinguishes the current experiments from our earlier work on graphite (9,12), where the in-plane phonon frequencies are so large, effectively only zero point motion is present in all but the zone-center acoustic modes before photoexcitation at 300 K. Here, thermal fluctuations of the lattice along all phonon coordinates are present before photoexcitation. TDS intensity provides a measure of the amplitude of these fluctuations at all phonon momenta.…”

“…The intensity of first-order, thermal-equilibrium diffuse scattering (TDS) at temperature T is given by where n j ( q ) = coth (ℏω j ( q )/2 k B T ) and ω j ( q ) are the occupancy and frequency of the phonon mode with wave vector q in branch j , respectively. is the one-phonon structure factor, which weights the contribution of each phonon according to the projection of its polarization vector onto q (see section S3) ( 9 , 12 ). For the case of low-frequency phonons (ℏω ≪ k B T ), Eq.…”

“…Figure 1E shows a schematic of the experimental geometry used to perform the UEDS measurements. We have previously shown that UEDS provides a momentum-resolved view of phonon dynamics ( 9 , 12 ) in a pump-probe configuration with ~100-fs time resolution ( 37 ). Here, we show that UEDS also allows the separation of impulsive changes to the real part of χ( q ) induced directly by photo-doping from the subsequent coupling of electronic excitation energy into the phonon system.…”

Bypassing the Structural Bottleneck in the Ultrafast Melting of Electronic Order

“…Two types of phonon modes with strong-coupling behavior and vibrational periods short enough to be compatible with the observed fast disordering are likely to be important: high-frequency (15 THz ≤ f < 2Δ 0 =h ≈ 29 THz) "phase phonons" which are coupled to oscillations in the phase of the electronic order parameter of Rb 0.3 MoO 3 [32,51,52], and the 28 THz (940 cm −1 ) Mo-O stretching mode, which is sensitive to the CDW transition [53,54]. The elucidation of the specific underlying lattice dynamics, however, is beyond the capabilities of trARPES and calls for a direct probing of phonon couplings and populations by ultrafast diffuse scattering techniques [55]. We speculate that the rapid atomic disordering due to mode-selective emission of (high-frequency) CDW-coupled phonons by hot electrons, as uncovered here, may be a more generic phenomenon [12,56] than the recently demonstrated collective launch of incoherent phonons driven by an ultrafast change to a highly anisotropic, flat lattice potential [30].…”

Toward nonthermal control of excited quantum materials: framework and investigations by ultrafast electron scattering and imaging

“…This can be understood by mapping the unfolding energy landscape involving the long-wave state evolution to the corresponding changes in the lattice field. The relevant lattice dynamics are governed by the momentum-dependent lattice potential expressed in the phonon dispersion curves (Figure 1b), which shift from those of the normal (T > T c ; solid lines) state to the brokensymmetry phase (T < T c ; dashed lines) with a mode softening at phonon momentum wavevector q ∼ Q which may be probed via the inelastic and diffuse scattering spectrum [52][53][54][55][56][57][58][59]. As the lattice potential changes leveled at the electronic scale is assumed to be nearly instantaneous, the soft modes in the critical regime (colored in red where the dispersion curves drop in frequency, ω) cannot respond adiabatically.…”