Exciton-phonon cooperative mechanism of the triple-$q$ charge-density-wave and antiferroelectric electron polarization in TiSe$_2$

TL;DR

This study reveals that in monolayer TiSe₂, the charge-density-wave state is stabilized by cooperative electron-phonon and excitonic interactions, leading to a bond-type CDW with antiferroelectric polarization.

Contribution

It demonstrates the combined role of electron-phonon coupling and intersite Coulomb interactions in stabilizing the triple-q CDW in TiSe₂, supported by first-principles calculations and spectral analysis.

Findings

Softening of transverse phonon modes at M points triggers CDW formation.

Intersite Coulomb interactions induce excitonic instability.

The CDW state exhibits bond-type order with vortex-like antiferroelectric polarization.

Abstract

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe$_2$ 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 TiSe$_2$ 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 TiSe$_2$. 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 TiSe$_2$ is of a bond-type and induces a vortex-like antiferroelectric polarization in the kagome network of Ti atoms.