Translation symmetry-breaking order is assumed to be suppressed by the lack of Fermi surface nesting near certain higher-order Van Hove singularities (HOVHS). We show that the anisotropic band-flattening inherent to such HOVHS, combined with broadening of the Fermi surface due to elevated critical scales, results in the Fermi surface becoming approximately nested at a wave vector unrelated to the precise shape of the Fermi surface—leading to a $\sqrt{3}\times \sqrt{3}$ Kekulé density wave formation. The effect is demonstrated using unbiased renormalization group calculations for a model of the breathing kagome lattice. Our mechanism—termed diffuse nesting—represents an entirely new notion in the study of Fermi surface instabilities.

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• Charge density waves
• Nesting
• Phase diagrams
• Spinless fermions
• Van Hove singularity
• Kagome lattice
• Kagome metal
• Extended Hubbard model
• Functional renormalization group
• Tight-binding model