Enhanced nematicity emerging from higher-order van Hove singularities

Abstract

Motivated by the experimental identification of a higher-order van Hove singularity (VHS) in AV${}_3$Sb${}_5$ kagome metals, we study electronic instabilities of 2D lattice models with higher-order VHS and flavor degeneracy. In contrast to conventional VHSs, the larger power-law density of states and the weaker nesting propensity of higher-order VHSs conspire together to generate distinct competing instabilities. After discussing the occurrence of higher-order VHSs on square and kagome lattice models, we perform unbiased renormalization group calculations to study competing instabilities and find a rich phase diagram containing ferromagnetism, anti-ferromagnetism, superconductivity and Pomeranchuk orders. Remarkably, there is a generic transition from superconductivity to a $d$-wave Pomeranchuk order with increasing flavor number. Implications for the intriguing quantum states of AV${}_3$Sb${}_5$ kagome metals are also discussed.

arXiv comment14 pages, 10 figures

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• High-order Van Hove singularities and their connection to flat bands
• Three-dimensional higher-order saddle points induced flat bands in Co-based kagome metals
• High-order van Hove singularities and nematic instability in the kagome superconductor CsTi${}_3$Bi${}_5$
• Inversion and Tunability of Van Hove Singularities in $A$V${}_3$Sb${}_5$ ($A$ = K, Rb, and Cs) kagome metals
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering