# Amplitude dynamics of charge density wave in LaTe$_3$: theoretical description of pump-probe experiments

## TL;DR

This paper develops a theoretical model combining Ginzburg-Landau equations and a three-temperature approach to describe the ultrafast dynamics of charge density waves in LaTe$_3$ following photoexcitation, matching experimental observations.

## Contribution

It introduces a coupled dynamical model for CDW amplitude evolution that integrates electronic and lattice temperature effects, providing a comprehensive description of pump-probe experiment results.

## Key findings

- Model accurately reproduces experimental CDW amplitude dynamics.
- Good agreement with ultrafast electron diffraction data.
- Provides insights into the interplay of electronic and lattice responses.

## Abstract

We formulate a dynamical model to describe a photo-induced charge density wave (CDW) quench transition and apply it to recent multi-probe experiments on LaTe$_3$ [A. Zong et al., Nat. Phys. 15, 27 (2019)]. Our approach relies on coupled time-dependent Ginzburg-Landau equations tracking two order parameters that represent the modulations of the electronic density and the ionic positions. We aim at describing the amplitude of the order parameters under the assumption that they are homogeneous in space. This description is supplemented by a three-temperature model, which treats separately the electronic temperature, temperature of the lattice phonons with stronger couplings to the electronic subsystem, and temperature of all other phonons. The broad scope of available data for LaTe$_3$ and similar materials as well as the synergy between different time-resolved spectroscopies allow us to extract model parameters. The resulting calculations are in good agreement with ultra-fast electron diffraction experiments, reproducing qualitative and quantitative features of the CDW amplitude evolution during the initial few picoseconds after photoexcitation.