Electronic instabilities at higher-order Van Hove singularity filling

Motived by the experimental discovery of higher-order Van Hove (HOVH) singularities in AV3Sb5 kagome metals, we study the instabilities in 2D systems with HOVH singularities and orbital degeneracy. In contrast to conventional Van Hove singularities, larger power-law divergent density of states, together with weaker nesting feature in higher-order Van Hove singularities, conspire to generate distinct competing instabilities. We performed unbiased renormalization group calculations and find a competition between anti-ferromagnetic and chiral superconductivity or Pomeranchuk order with initial repulsive interactions. In the square lattice with two HOVH singularities, our calculations reveal a phase transition from the $d$-wave superconductivity to the uniform charge order or$d$-wave Pomeranchuk order. In the hexagonal lattice with three HOVH singularities, a negative intra-patch interaction will yield superconductivity or Pomeranchuk instability. Implications for correlated states in AV3Sb5 kagome metals are also discussed.