Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone

TL;DR

This paper uses parquet renormalization group analysis to identify possible weak-coupling electronic instabilities in systems with multiple high-order Van Hove points, revealing five distinct correlated phases inspired by twisted bilayer graphene.

Contribution

It introduces a comprehensive RG framework to analyze weak-coupling instabilities with multiple high-order Van Hove points, uncovering five novel correlated phases.

Findings

Identified five stable correlated phases including various superconducting and magnetic orders.

Demonstrated stability of the phase diagram against band deformations.

Applied the analysis to a model inspired by twisted bilayer graphene.

Abstract

We analyze the weak-coupling instabilities that may arise when multiple high-order Van Hove points are present inside the Brillouin zone. The model we consider is inspired by twisted bilayer graphene, although the analysis should be more generally applicable. We employ a parquet renormalization group analysis to identify the leading weak-coupling instabilities, supplemented with a Ginzburg-Landau treatment to resolve any degeneracies. Hence we identify the leading instabilities that can occur from weak repulsion with the power-law divergent density of states. Five correlated phases are uncovered along distinct stable fixed trajectories, including $s$-wave ferromagnetism, $p$-wave chiral/helical superconductivity, $d$-wave chiral superconductivity, $f$-wave valley-polarized order, and $p$-wave polar valley-polarized order. The phase diagram is stable against band deformations which preserve the high-order Van Hove singularity.