Gate-tunable topological phases in superlattice modulated bilayer graphene

Superlattice potential modulation can produce flat minibands inBernal-stacked bilayer graphene. In this work we study how band topology andinteraction-induced symmetry-broken phases in this system are controlled bytuning the displacement field and the shape and strength of the superlatticepotential. We use an analytic perturbative analysis to demonstrate thattopological flat bands are favored by a honeycomb-lattice-shaped potential, andnumerics to show that the robustness of topological bands depends on both thedisplacement field strength and the periodicity of the superlattice potential.At integer fillings of the topological flat bands, the strength of thedisplacement field and the superlattice potential tune phase transitionsbetween quantum anomalous Hall insulator, trivial insulator, and metallicstates. We present mean-field phase diagrams in a gate voltage parameter spaceat filling factor $\nu=1$, and discuss the prospects of realizing quantumanomalous Hall insulators and fractional Chern insulators when the superlatticepotential modulation is produced by dielectric patterning or adjacent moir\'ematerials.