# Charge Density Wave Hampers Exciton Condensation in 1T-TiSe$_2$

## TL;DR

This paper uses first-principles calculations to analyze how charge density waves and temperature affect exciton condensation in TiSe$_2$, revealing mechanisms that hinder the formation of exciton condensates.

## Contribution

It provides the first ab initio atomic-level analysis of exciton condensation suppression due to charge density waves and electronic temperature effects in TiSe$_2$.

## Key findings

- Charge density waves introduce a gap that hampers exciton formation.
- Finite electronic temperature causes dissipation, preventing condensation above T_c.
- Soft plasmon modes are linked to interband electronic transitions, not simple models.

## Abstract

The Bose-Einstein condensation of excitons continues to garner immense attention as a prototypical example for observing emergent properties from many-body quantum effects. In particular, Titanium Diselenide (TiSe$_2$) is a promising candidate for realizing exciton condensation and was experimentally observed only very recently. Surprisingly, the condensate was experimentally characterized by a soft plasmon mode that only exists near the transition temperature, $T_c$, of the charge density wave (CDW). Here, we characterize and analyze the experimental spectra using linear-response time-dependent density functional theory and find that the soft mode can be attributed to interband electronic transitions. At the CDW state below $T_c$, the periodic lattice distortions hamper the spontaneous formation of the exciton by introducing a CDW gap. The band gap raises the soft mode and merges it into the regular plasmon. Our surprising results contradict previous simplistic analytical models commonly used in the scientific literature. In addition, we find that a finite electronic temperature, $T_e$, introduces a dissipation channel and prevents the condensation above $T_c$. The combined effect of the CDW and $T_e$ explains the fragile temperature-dependence of the exciton condensation. Taken together, our work provides the first \textit{ab initio} atomic-level framework for rationalizing recent experiments and further manipulating exciton condensates in TiSe$_2$.