Exciton-phonon cooperative mechanism of the triple-q charge-density-wave and antiferroelectric electron polarization in TiSe2

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe2 using a realistic multiorbital d-p model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti 3d and Se 4p orbitals in the monolayer TiSe2 on the basis of the first-principles band-structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the M point of the Brillouin zone. The stability of the triple-q CDW state is thus examined to show that the transverse phonon modes at the M-1, M-2, and M-3 points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se 4p and conduction Ti 3d bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-q CDW state in TiSe2. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in TiSe2 is of a bond type and induces a vortexlike antiferroelectric polarization in the kagome network of Ti atoms.