Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moir\'e Flatbands

TL;DR

This paper explores the physics of Coulomb interactions in Moiré flatbands, revealing how a particle-hole duality approach uncovers emergent Fermi liquids and fractional Chern insulators in twisted bilayer graphene and related systems.

Contribution

It introduces a dual hole description for strongly interacting flatbands, enabling perturbative analysis and predicting emergent Fermi liquids and fractional Chern insulators.

Findings

Emergent Fermi liquid states at 1/3 and 2/3 fillings.

Non-Fermi liquid behavior at lower fillings.

Microscopic evidence for fractional Chern insulators in twisted bilayer graphene.

Abstract

Moir\'e flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moir\'e flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. In experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent interaction-driven Fermi liquid states at electronic filling fractions down to around $1/3$ and $2/3$ respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behavior. Most saliently, we provide microscopic evidence that high temperature fractional Chern insulators can form in twisted bilayer graphene aligned with hexagonal boron nitride.