Higher-order gaps in the renormalized electronic band structure of doubly aligned bilayer graphene hBN moiré

Abstract This article presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. By utilizing two interfering moire′ potentials, we generate a supermoire′ pattern which renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher-order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we used electronic transport measurements to identify the position of these gaps as functions of the carrier density and establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides conclusive evidence of quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills essential gaps in understanding the band structure engineering of Dirac fermions by a doubly periodic superlattice spinor potential.