# Competing phases of interacting electrons on triangular lattices in moir\'e heterostructures

## TL;DR

This paper investigates the competing electronic phases in moiré heterostructures on triangular lattices, revealing tendencies towards density waves, Chern insulators, and topological superconductivity through a comprehensive renormalization group analysis.

## Contribution

It introduces an unbiased functional renormalization group study of an extended Hubbard model for moiré heterostructures, identifying novel phases and their dependence on filling and interactions.

## Key findings

- Hund-like couplings induce density wave instabilities.
- SU(4) exchange promotes a Chern insulator phase.
- Topological $d\u00b1 id$ and $f$-wave superconductivity are found.

## Abstract

We study the quantum many-body instabilities of interacting electrons with SU(2)$\times$SU(2) symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moir\'e heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions and analyze the different ordering tendencies with the help of an unbiased functional renormalization group approach. We find three classes of instabilities controlled by the filling and bare interactions. For a nested Fermi surface at van-Hove filling, Hund-like couplings induce a weak instability towards spin or orbital density wave phases. An SU(4) exchange interaction moves the system towards a Chern insulator, which is robust with respect to perturbations from Hund-like interactions or deviations from perfect nesting. Further, in an extended range of fillings and interactions, we find topological $d\pm id$ and (spin-singlet)-(orbital-singlet) $f$-wave superconductivity.