Motivated by the experimental identification of a higher-order van Hove singularity (VHS) in AV3Sb5 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 AV3Sb5 kagome metals are also discussed.
@article{arxiv.2302.02906,
title = {Enhanced nematicity emerging from higher-order van Hove singularities},
author = {Xinloong Han and Andreas P. Schnyder and Xianxin Wu},
journal= {arXiv preprint arXiv:2302.02906},
year = {2023}
}