Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: An emergent gauge picture

The recent experimental discovery of the zero-field fractional Chern insulator (FCI) in twisted MoTe₂ moir\'e superlattices has sparked immense interest in this exotic topological quantum state. The FCI has also been observed in previous experiments in magic angle twisted bilayer graphene (TBG) under a finite magnetic field of about 5 Tesla. Generally, the stabilization of FCI requires fine-tuning the topological band to satisfy certain conditions. It would still be helpful to have an intuitive picture to understand the different behaviors in twisted MoTe₂ and TBG. Here, we compare them through the lens of emergent gauge fields. In TBG, the system can be mapped to two Dirac fermions coupled to emergent gauge fields with opposite signs. In contrast, the twisted MoTe₂ reduces to a hole with parabolic dispersion coupled to an emergent gauge field. Although the stabilization of FCI generally requires fine-tuning of the band dispersion and its quantum geometry, this contrasting gauge structure provides another perspective on the observed difference: the zero-field FCI is stable in MoTe₂ but absent in TBG. Based on this understanding, we will explore potential strategies for stabilizing FCI in both moir\'e superlattices.