Giant Kohn anomaly and chiral phonons in the charge density wave phase of 1H-NbSe$_2$

TL;DR

This paper reveals that in monolayer 1H-NbSe$_2$, a longitudinal optical phonon exhibits a giant Kohn anomaly and circular polarization, driven by electron-phonon interactions, elucidating the nature of charge density waves.

Contribution

It provides the first detailed computational evidence that a longitudinal optical phonon, not an acoustic mode, softens via a Kohn ladder mechanism in 1H-NbSe$_2$.

Findings

The relevant soft mode is a longitudinal optical phonon, not an acoustic mode.

The phonon softening occurs through anti-crossing with multiple bands, forming a Kohn ladder.

The softened phonons are circularly polarized.

Abstract

Despite extensive investigations, many aspects of charge density waves (CDWs) remain elusive, especially the relative roles of electron-phonon coupling and Fermi surface nesting as the underlying driving mechanisms responsible for the emergence of the CDW vector $Q_{CDW}$. It is puzzling that even though electrons interact strongly with optical phonons in many correlated systems, the actual mode softening is of an acoustic mode. Here we consider monolayer 1H-NbSe$_2$ as an exemplar system, and through an accurate computation of the phonon self-energy, including its off-diagonal components, we provide compelling evidence that the relevant mode is a longitudinal optical phonon that softens by anti-crossing several intervening phonon bands, i.e. a Kohn ladder which has been only observed previously in high temperature superconductors. We also show that $Q_{CDW}$ is fixed by the convolution of the susceptibility and electron-phonon coupling, and that the softened phonons are circularly polarized.