Chiral charge order in 1$T$-TiSe$_2$: importance of lattice degrees of freedom

TL;DR

This paper investigates the microscopic origin of chiral charge order in 1T-TiSe2, emphasizing the crucial role of lattice degrees of freedom and electron-phonon interactions in stabilizing this phenomenon.

Contribution

It introduces a theoretical model incorporating electron bands, Coulomb interactions, and electron-phonon coupling to explain chiral charge order in TiSe2.

Findings

Chiral charge order arises from combined electron-hole pairing and lattice deformation.

Both electron-phonon and phonon-phonon interactions are essential for stability.

The model's phase diagram and interaction constants are provided for TiSe2.

Abstract

We address the question of the origin of the recently discovered chiral property of the charge-density-wave phase in 1$T$-TiSe$_2$ which so far lacks a microscopic understanding. We argue that the lattice degrees of freedom seems to be crucial for this novel phenomenon. We motivate a theoretical model that takes into account one valence and three conduction bands, a strongly screened Coulomb interaction between the electrons, as well as the coupling of the electrons to a transverse optical phonon mode. The Falicov-Kimball model extended in this way possesses a charge-density-wave state at low temperatures, which is accompanied by a periodic lattice distortion. The charge ordering is driven by a lattice deformation and electron-hole pairing (excitonic) instability in combination. We show that both electron-phonon interaction and phonon-phonon interaction must be taken into account at least up to quartic order in the lattice displacement to achieve a stable chiral charge order. The chiral property is exhibited in the ionic displacements. Furthermore, we provide the ground-state phase diagram of the model and give an estimate of the electron-electron and electron-phonon interaction constants for 1$T$-TiSe$_2$.