Soft Phonon Charge-Density-Wave Formation in the Kagome Metal KV_{3}Sb_{5}

A range of unusual emergent behaviors have been reported in the charge-density-wave (CDW) state of the AV_{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_{CDW}=78  K. The intensity of soft phonons exhibits 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 AV_{3}Sb_{5}. Using first-principles calculations, we find that the momentum-dependent electron-phonon coupling (EPC) peaks at L and exhibits the same in-plane anisotropy as the phonon softening. Conversely, the electronic susceptibility does not peak 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.