Excitons and Optical Response in Excitonic Insulator Candidate TiSe$_2$

Abstract

The origin of the charge density wave (CDW) phase in TiSe$_2$ is a highly debated topic, with lattice and excitonic correlations proposed as the main driving mechanisms. One of the proposed scenarios is the excitonic insulator (EI) mechanism, where soft electronic mode drives the phase transition. However, the existence of this purely electronic mode is controversial. Here, we perform fully ab-initio calculations of the electron excitation spectra in TiSe$_2$ with electron-hole excitonic effects included via Bethe-Salpeter equations. In the normal high-temperature phase the excitation spectra is dominated by the exciton mode at 1.6 eV, while no well-defined soft electronic modes that could support the EI phase are present. In the CDW phase, the structural distortions induce a CDW band-gap opening between Ti-$d$ and Se-$p$ states, which supports the formation of the two low-energy excitonic modes in the optical spectrum at 0.4 eV and 80 meV. Close to the transition temperature $T_{\rm CDW}$, these two excitonic modes are softened and approach zero energy. These results suggest that the EI mechanism is not a main driving force in the formation of the CDW phase in TiSe$_2$, but there is a region in the phase diagram near $T_{\rm CDW}$ where EI fluctuations could be relevant.