Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene

TL;DR

This study uses exact diagonalization to explore the competition between fractional Chern insulator and charge-density-wave phases in twisted bilayer graphene, revealing phase diagrams consistent with experimental observations.

Contribution

It provides the first comprehensive analysis of the interplay between fractional Chern insulators and charge-density waves in realistic twisted bilayer graphene models.

Findings

Identification of competing phases at various fillings

Phase diagram aligning with experimental data

Role of Berry curvature in phase selection

Abstract

We perform an extensive exact diagonalization study of interaction driven insulators in spin- and valley-polarized moir\'{e} flat bands of twisted bilayer graphene aligned with its hexagonal boron nitride substrate. In addition to previously reported fractional Chern insulator phases, we provide compelling evidence for competing charge-density-wave phases at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection. The resulting phase diagram features remarkable agreement with experimental findings in a related moir\'{e} heterostructure and affirms the relevance of our results beyond the scope of graphene based materials.