  Van der Waals heterostructures comprise a new class of artificial materials
formed by stacking atomically-thin planar crystals. Here, we demonstrate band
structure engineering of a van der Waals heterostructure composed of a
monolayer graphene flake coupled to a rotationally-aligned hexagonal boron
nitride substrate. The spatially-varying interlayer atomic registry results
both in a local breaking of the carbon sublattice symmetry and a long-range
moir\'e superlattice potential in the graphene. This interplay between short-
and long-wavelength effects results in a band structure described by isolated
superlattice minibands and an unexpectedly large band gap at charge neutrality,
both of which can be tuned by varying the interlayer alignment.
Magnetocapacitance measurements reveal previously unobserved fractional quantum
Hall states reflecting the massive Dirac dispersion that results from broken
sublattice symmetry. At ultra-high fields, integer conductance plateaus are
observed at non-integer filling factors due to the emergence of the Hofstadter
butterfly in a symmetry-broken Landau level.

Mesoscale and Nanoscale Physics