Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice.

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that 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 use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice.

We present experimental findings on electron-electron scattering in two-dimensional moiré heterostructures with a tunable Fermi wave vector, reciprocal lattice vector, and band gap. We achieve this in high-mobility aligned heterostructures of bilayer graphene (BLG) and hBN. Around the half-full point, the primary contribution to the resistance of these devices arises from Umklapp electron-electron (Uee) scattering, making the resistance of graphene/hBN moiré devices significantly larger than that of non-aligned devices (where Uee is forbidden). We find that the strength of Uee scattering follows a universal scaling with Fermi energy and is nonmonotonically dependent on the superlattice period. The Uee scattering can be tuned with the electric field and is affected by layer polarization of BLG. It has a strong particle-hole asymmetry; the resistance when the chemical potential is in the conduction band is significantly lower than when it is in the valence band, making the electron-doped regime more practical for potential applications.