Theoretical description of time-resolved photoemission in charge-density-wave materials out to long times

TL;DR

This paper develops a semiclassical Monte Carlo method to model long-time nonequilibrium dynamics in charge-density-wave materials after pump excitation, capturing lattice-electron interactions and amplitude mode ringing observed experimentally.

Contribution

It introduces a computationally efficient semiclassical approach to simulate long-time charge-density-wave dynamics, including lattice relaxation and amplitude mode ringing, which was previously unexplained microscopically.

Findings

Successfully models long-time lattice relaxation in CDW materials.

Reproduces experimentally observed amplitude mode ringing.

Identifies regimes of pump-induced CDW order inversion.

Abstract

We describe coupled electron-phonon systems semiclassically - Ehrenfest dynamics for the phonons and quantum mechanics for the electrons - using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is quite accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds) enabling us to model pump-probe experiments of a charge density wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the driving of the electrons by the pump field. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment, but never successfully explained by microscopic theory.