Inducing Flat Chern Bands in Bilayer Graphene Exposed to a Superlattice Potential

It was recently argued that Bernal stacked bilayer graphene exposed to a 2D superlattice potential exhibits a variety of intriguing behaviors [1]. Chief among them is the appearance of flat Chern bands – with the possibility of Chern numbers C such that |C|>1 – that are favorable to the appearance of fractional Chern insulator states. Here, we explore extensions of the model of Ghorashi et al. [1] to find additional means of inducing flat Chern bands. First, we endow the superlattice potential with a tunable phase shift. The phase controls the locations and numbers of maxima and minima of the potential within the superlattice unit cell, while also allowing us to keep track of the changes in Chern numbers of the low-energy bands. Finally, we study the effects of out-of-plane orbital magnetic fields featuring zero as well as single flux quanta in the superlattice unit cell.

[1] Ghorashi et al., Phys. Rev. Lett. 130, 196201