Charge-density wave induced by combined electron-electron and electron-phonon interactions in 1$T$-TiSe$_2$: A variational Monte Carlo study

TL;DR

This study uses variational Monte Carlo to show that charge-density waves in 1T-TiSe2 arise from a cooperative effect of electron-electron and electron-phonon interactions, favoring a BEC-like electron-hole pairing mechanism.

Contribution

It provides a quantum mechanical treatment of both electronic and lattice degrees of freedom, revealing the importance of combined interactions in CDW formation in 1T-TiSe2.

Findings

Cooperative electron-electron and electron-phonon interactions induce CDW.

Pure exciton condensation without lattice distortion is unlikely.

Strong-coupling BEC-like electron-hole pairing dominates in the CDW phase.

Abstract

To clarify the origin of a charge-density wave (CDW) phase in 1$T$-TiSe$_2$, we study the ground state property of a half-filled two-band Hubbard model in a triangular lattice including electron-phonon interaction. By using the variational Monte Carlo method, the electronic and lattice degrees of freedom are both treated quantum mechanically on an equal footing beyond the mean-field approximation. We find that the cooperation between Coulomb interaction and electron-phonon interaction is essential to induce the CDW phase. We show that the "pure" exciton condensation without lattice distortion is difficult to realize under the poor nesting condition of the underlying Fermi surface. Furthermore, by systematically calculating the momentum resolved hybridization between the two bands, we examine the character of electron-hole pairing from the viewpoint of BCS-BEC crossover within the CDW phase and find that the strong-coupling BEC-like pairing dominates. We therefore propose that the CDW phase observed in 1$T$-TiSe$_2$ originates from a BEC-like electron-hole pairing.