# Ultrafast charge ordering by self-amplified exciton-phonon dynamics in TiSe$_2$

## TL;DR

This study uses real-time simulations to disentangle and clarify the ultrafast interplay between excitonic and lattice dynamics in TiSe$_2$, revealing how they mutually amplify to invert charge density wave order.

## Contribution

It provides the first detailed temporal separation of exciton and phonon contributions in TiSe$_2$, demonstrating their sequential and self-amplifying roles in CDW dynamics.

## Key findings

- Exciton order is disrupted within 20 fs by laser pulses.
- Electronic order weakening triggers ionic movements opposite to original lattice distortions.
- The interplay leads to a complete inversion of charge density wave order.

## Abstract

The origin of charge density waves (CDW) in TiSe$_2$ has long been debated, mainly due to the difficulties in identifying the timescales of how and when the excitonic pairing and electron-phonon coupling (EPC) come into play. Without a proper time resolution and microscopic mechanism, one has to assume simultaneous appearance of CDW and periodic lattice distortions (PLD). Here, we accomplish a complete separation of exciton and PLD dynamics and unravel their interplay in the ultrafast time domain in our real-time time-dependent density functional theory simulations. We find that laser pulses knock off the exciton order and induce a homogeneous bonding-antibonding transition in the initial 20 fs, then the weakened electronic order triggers ionic movements antiparallel to the original PLD. The EPC comes into play after the initial 20~fs, and the two processes mutually amplify each other leading to a complete inversion of CDW ordering. The self-amplified dynamics reproduces the evolution of band structures in excellent agreement with ultrafast photoemission experiment. Hence we resolve the key processes in the initial dynamics of CDW that help elucidate the mechanism underlying the long debated problem.