Hofstadter's Butterfly in a Lithographically Defined Super-Lattice

We will present magnetotransport measurements of a gated superlattice formed on hBN encapsulated graphene in which a local gate provides a lattice-like external potential. Recent improvements in lithography have allowed for the patterning of periodic lattice structures with lattice constants of 40 nm or less. While the Hofstadter fractal energy spectrum has been studied previously through the Moire interference pattern between graphene and hBN, it has not been observed in such a tunable environment. Our multi-gate structure allows us to independently set carrier density and lattice strength, allowing us to investigate the competition between multiple allowed states associated with different lattices in our 2DEG. By comparing different lattice geometries we will also present a richer understanding of how lattice symmetry alters the Hofstadter energy spectrum.