Fermi surface geometry and momentum dependent electron-phonon coupling drive the charge density wave in quasi-1D ZrTe$3$

TL;DR

This study shows that in ZrTe3, charge density wave formation is primarily driven by momentum-dependent electron-phonon coupling, with Fermi surface geometry playing a supporting role, as revealed by first-principles calculations.

Contribution

It demonstrates that momentum-dependent electron-phonon coupling, combined with Fermi surface effects, is the main driver of the CDW in ZrTe3, clarifying the lattice dynamics involved.

Findings

Fermi surface is accurately reproduced only with Hubbard interaction on Te 5p orbitals.

A soft harmonic phonon mode appears at the CDW wavevector due to electron-phonon coupling.

Electron-phonon coupling variations dominate over electronic effects in driving the CDW.

Abstract

ZrTe$_3$ is a prototypical quasi-one-dimensional compound undergoing a charge density wave transition via a very sharp Kohn anomaly in phonon momentum space. While Fermi surface geometry has long been considered the primary driver of the instability, a full understanding of the lattice dynamics and electron-phonon role has remained elusive. Our first principles calculations in the high-symmetry phase show that the Fermi surface is correctly reproduced only when the Hubbard interaction on the Te $5p$ orbitals is included, which in turn is essential for the appearance of a soft harmonic phonon mode at the CDW wavevector. Analyzing the mode and momentum dependence of the electron-phonon coupling, we find that its variations with phonon momentum dominate over electronic effects. These results identify unambiguously the CDW origin in ZrTe$_3$ as a cooperative effect of Fermi surface geometry and momentum-dependent electron-phonon coupling, with the latter playing the leading role. We further determine the atomic structure in the low-symmetry CDW phase, revealing a nonchiral modulation. The mechanisms revealed in our work are directly relevant to other quasi-1D systems, including trichalcogenides and compounds hosting Peierls-like chains.