Fermi-surface driven frustrations in charge ordered kagome metal LuNb₆Sn₆

The charge density wave (CDW), a translational symmetry breaking electronic liquid, plays a pivotal role in correlated quantum materials, such as high-T_c superconductors and topological semimetals. Recently, CDWs that possibly intertwine with superconductivity and magnetism are observed in various kagome metals. However, the nature of CDWs and the role of the Fermi-surface (FS) topology in these materials remain an unresolved challenge. In this paper, we reveal the formation of CDWs in the newly discovered kagome metal LuNb₆Sn₆. We observe a “yield sign”-like hollow triangular diffuse scattering pattern and nearly complete softening of a flat optical phonon band near Q_H = (1/3, 1/3, 1/2). The scattering intensity of the diffuse scattering displays divergent behavior as decreasing temperature until T_CDW = 70 K, where a competing CDW at Q_CDW = (1/3, 1/3, 1/3) emerges. Combined with scanning tunneling microscopy/spectroscopy and first-principles calculations, our observations support a Fermi-surface driven frustration that suppresses the leading CDW instability at Q_H. This frustration is relieved by the emergence of a subleading CDW at Q_CDW. These results provide insights into the interplay between the Fermi surface, strong electron-phonon coupling, and charge density wave formation in quantum materials.