Soft Phonon Charge-Density Wave Formation in the Kagome Metal KV$_3$Sb$_5$

TL;DR

This study reveals that the charge-density wave in KV$_3$Sb$_5$ forms through phonon softening at the $L$-point, driven by momentum-dependent electron-phonon coupling, indicating an unconventional CDW mechanism similar to transition metal dichalcogenides.

Contribution

The paper demonstrates phonon softening at the CDW transition in KV$_3$Sb$_5$ and links it to momentum-dependent electron-phonon coupling through combined experimental and first-principles analysis.

Findings

Phonons soften to zero energy at the $L$-point around 78 K.

In-plane anisotropy of soft phonons extends over larger momentum range along $L$-$A$.

Electron-phonon coupling peaks at $L$, correlating with phonon softening.

Abstract

A range of of unusual emergent behaviors have been reported in the charge-density wave (CDW) state of the $A$V$_3$Sb$_5$ ($A=~$K, Rb, Cs) kagome metals, including a CDW formation process without soft phonons, which points to an unconventional CDW mechanism. Here, we use inelastic x-ray scattering to show that the CDW in KV$_3$Sb$_5$ forms via phonons that soften to zero energy at the CDW ordering vector ($L$-point) around $T_{\rm CDW}=78$~K. The intensity of soft phonons exhibit a remarkable in-plane anisotropy, extending over a much larger momentum range along $L$-$A$ relative to $L$-$H$, which leads to diffuse scattering common among $A$V$_3$Sb$_5$. Using first-principles calculations, we find that the momentum-dependent electron-phonon coupling (EPC) is peaked at $L$ and exhibits the same in-plane anisotropy as the phonon softening. Conversely, the electronic susceptibility is not peaked at $L$ and shows the opposite in-plane anisotropy. Our findings favor momentum-dependent EPC as the driving mechanism of the CDW in KV$_3$Sb$_5$, with a CDW formation process similar to that of transition metal dichalcogenides.