Fractal Hofstadter Band Structure in Patterned Dielectric Superlattice Graphene Systems

The development and characterization of lithographically patterned dielectric superlattice systems are presented, which have enabled the first clear realization of fully developed fractal mini-gaps owing to the interplay between a quantizing magnetic field and a lithographically defined spatial superlattice potential. Following a history of lateral superlattice gating on 2-D electron gas systems, we present patterned dielectric superlattice graphene systems of unmatched quality, allowing for the characterization of Hofstadter fractal band structure under triangular and square lattice geometries. Hexagonal boron nitride, graphene heterostructures are uniquely suited to integration with patterned gating structures, due to their high mobility and thin encapsulating dielectric environment. These systems have already been utilized for the observation of Hofstadter’s fractal spectrum through the moiré superlattice effect, but such systems are limited in their tunability. The patterned dielectric superlattice allows for control of the superlattice geometry, polarity, and strength. Utilizing this control, we compare the resultant fractal spectra from both triangular and square superlattice potentials, which confer unique gap structures in agreement with their lattice symmetry. More generally, patterned dielectric superlattices can be used to generate a variety of spatially dependent scalar potentials onto van der Waals heterostructures with length scales of order 10nm, while maintaining low disorder.