  Graphene superlattices were shown to exhibit high-temperature quantum
oscillations due to periodic emergence of delocalized Bloch states in high
magnetic fields such that unit fractions of the flux quantum pierce a
superlattice unit cell. Under these conditions, semiclassical electron
trajectories become straight again, similar to the case of zero magnetic field.
Here we report magnetotransport measurements that reveal second, third and
fourth order magnetic Bloch states at high electron densities and temperatures
above 100 K. The recurrence of these states creates a fractal pattern
intimately related to the origin of Hofstadter butterflies. The hierarchy of
the fractal states is determined by the width of magnetic minibands, in
qualitative agreement with our band structure calculations.
