Development of an ab initio method for exciton condensation and its application to TiSe_{2}

Abstract

Exciton condensation is a phenomenon that indicates the spontaneous formation of electron-hole pairs, which can lead to a phase transition from a semimetal to an excitonic insulator by opening a gap at the Fermi surface. Although the idea of an excitonic insulator has been proposed for several decades, current theoretical approaches can only provide qualitative descriptions, and a quantitative predictive tool is still lacking. To shed light on this issue, we developed an ab initio method based on finite-temperature density functional theory and many-body perturbation theory to calculate the critical behavior of exciton condensation. Utilizing our methodology on monolayer TiSe_{2}, we identify a phase transition involving lattice distortion and nontrivial electron-hole correlation at a temperature exceeding the critical temperature of phonon softening. By breaking down the components within the gap equation, we demonstrate that exciton condensation, mediated by electron-phonon interaction, is the underlying cause of the charge-density-wave state observed in this compound. Overall, the methodology introduced in this work is general and sets the stage for searching for potential excitonic insulators in natural material systems.