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

## TL;DR

This paper develops a quantitative framework to analyze ultrafast electron diffuse scattering data, enabling the extraction of phonon populations and coupling constants across the Brillouin zone, demonstrated on graphite.

## Contribution

It introduces a detailed method for interpreting UEDS signals to determine phonon mode occupancies and coupling constants, advancing the understanding of lattice-charge interactions.

## Key findings

- Extracted momentum- and mode-dependent electron-phonon and phonon-phonon coupling constants.
- Determined the A1' phonon mode-projected electron-phonon coupling strength in graphite.
- Validated the method by comparing results with other techniques and simulations.

## 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 deconvolves 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 electron-phonon coupling strength $\langle g_{e,A_1'}^2 \rangle = 0.035 \pm 0.001$ eV$^2$ that is in agreement with other measurement techniques and simulations.