Interplay of fractional Chern insulator and charge density wave phases in twisted bilayer graphene

We perform an extensive exact diagonalization study of interaction-driven insulators in spin- and valley-polarized moire 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 moire heterostructure and affirms the relevance of our results beyond the scope of graphene-based materials.

Automated summary

An extensive study was conducted on interaction-driven insulators in spin- and valley-polarized moire flat bands of twisted bilayer graphene, revealing fractional Chern insulator phases and competing charge-density-wave phases. Analysis at different parameters highlighted the competition between these phases, with kinetic energy and Coulomb interaction strength playing crucial roles. The ground-state selection was intuitively understood to be driven by the interplay between single-particle and interaction-induced hole dispersion with the Berry curvature of the Chern bands. The resulting phase diagram showed remarkable agreement with experimental findings, extending the relevance of the results beyond graphene-based materials.