Enhanced nematicity emerging from higher-order van Hove singularities

TL;DR

This paper investigates how higher-order van Hove singularities in 2D lattice models lead to diverse electronic instabilities, including ferromagnetism, superconductivity, and Pomeranchuk orders, with implications for kagome metals.

Contribution

It introduces the study of higher-order VHS effects on electronic instabilities using renormalization group analysis, revealing a rich phase diagram and a transition from superconductivity to Pomeranchuk order.

Findings

Higher-order VHSs exhibit larger density of states and weaker nesting.

The phase diagram includes ferromagnetism, antiferromagnetism, superconductivity, and Pomeranchuk orders.

A transition from superconductivity to $d$-wave Pomeranchuk order occurs with increasing flavor number.

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.