Kekulé Order from Diffuse Nesting near Higher-Order Van Hove Points

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]×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.