The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating ∣C∣=2 dispersionless electronic bands when the skyrmion periodicity and the moir\'e periodicity are matched. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is \textit{bosonic}, characterized by electronic charge Q=2e, that is \textit{even} in units of electron charge e. The required skyrmion coupling strength triggering the topological phase transition is realistic, with its threshold estimated as low as 4~meV. The Hofstadter butterfly spectrum of this phase is different resulting in an unexpected quantum Hall conductance sequence ±h2e2,±h4e2,... for TBG with skyrmion order.
@article{arxiv.2111.10410,
title = {Unconventional Flat Chern Bands and 2$e$ Charges in Skyrmionic Moir\'e Superlattices},
author = {Yifei Guan and Oleg V. Yazyev and Alexander Kruchkov},
journal= {arXiv preprint arXiv:2111.10410},
year = {2021}
}