This paper investigates the band topology and interaction-induced symmetry-broken phases in Bernal-stacked bilayer graphene (BLG) modulated by a superlattice potential (SL-BLG). The authors use analytic perturbative analysis and numerical simulations to study how the displacement field and the shape and strength of the superlattice potential control these phases. They find that topological flat bands are favored by a honeycomb-lattice-shaped potential, and the robustness of these bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, phase transitions between quantum anomalous Hall insulator, trivial insulator, and metallic states occur. The paper presents mean-field phase diagrams in a gate voltage parameter space at filling factor \(\nu = 1\) and discusses the prospects for realizing quantum anomalous Hall insulators and fractional Chern insulators using dielectric patterning or adjacent moiré materials. The results suggest that SL-BLG can be a versatile platform for studying correlated and topological phases, with the potential for routine realization of quantum anomalous Hall insulators.This paper investigates the band topology and interaction-induced symmetry-broken phases in Bernal-stacked bilayer graphene (BLG) modulated by a superlattice potential (SL-BLG). The authors use analytic perturbative analysis and numerical simulations to study how the displacement field and the shape and strength of the superlattice potential control these phases. They find that topological flat bands are favored by a honeycomb-lattice-shaped potential, and the robustness of these bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, phase transitions between quantum anomalous Hall insulator, trivial insulator, and metallic states occur. The paper presents mean-field phase diagrams in a gate voltage parameter space at filling factor \(\nu = 1\) and discusses the prospects for realizing quantum anomalous Hall insulators and fractional Chern insulators using dielectric patterning or adjacent moiré materials. The results suggest that SL-BLG can be a versatile platform for studying correlated and topological phases, with the potential for routine realization of quantum anomalous Hall insulators.