Electron–hole instability in 1T-TiSe₂

In this paper, we address the question of the origin of the charge density wave instability in 1 T -TiSe 2 . We develop a model considering the direct Coulomb interaction between electrons and holes in the valence and conduction bands near the Fermi energy. Using the Bethe–Salpeter equation, we calculate the electron–hole correlator, which reveals an instability at low temperature leading to a transition toward a commensurate superstructure mediated by the electron–phonon coupling, in agreement with experiments. On the basis of this correlator, the electron self-energies are then calculated and the corresponding photoemission spectra are compared with the experimental ones, revealing good agreement. The signature of electron–hole fluctuations in photoemission is emphasized. Furthermore, we calculate the spectral function of the phonon mode, whose softening is experimentally observed at the transition.