Hofstadter's Butterfly in the strongly interacting regime

In 1976, Douglas Hofstadter predicted that in the presence of both a strong magnetic field, and a spatially varying periodic potential, Bloch electrons confined to a 2D quantum well exhibit a self-similar fractal energy spectrum known as the ``Hofstadter's Butterfly.'' In subsequent years, experimental discovery of the quantum Hall effect gave birth to an expansive field of research into 2D electronic systems in the presence of a magnetic field, however, direct confirmation of the fractal spectrum remained elusive. Recently we demonstrated that graphene, in which Bloch electrons can be described by Dirac fermions, provides a new opportunity to investigate this nearly 40 year old problem. In this talk I will discuss the experimental realization of Hofstader's butterfly by exploiting nano-scale interfacial effects between graphene and hexagonal boron nitride substrates, together with application of extremely high magnetic fields. Utilizing newly developed techniques to fabricate ultra-clean graphene devices, I will additionally demonstrate the capability to probe for the first time the effect of strong electron interactions within the fractal Hofstadter spectrum.