Engineering New Electronic States in Graphene Heterostructures: Massive Dirac Fermions and Hofstadter’s Butterfly

Van der Waals heterostructures represent a new and surprising direction in nanoscale device engineering: we stack isolated two-dimensional crystals to create layered structures with atomic precision. The layer-by-layer assembly allows us to introduce a new design parameter - the interlayer twist angle - which can have profound consequences for the engineering of electronic states based on tunable interactions between adjacent layers. In this talk, I will discuss recent experiments at MIT in which we have used a hexagonal boron nitride (hBN) layer to modify the electronic bands of monolayer graphene in a van der Waals heterostructure, inducing a sizable bandgap at the charge neutrality point and imparting a mass to the normally massless Dirac charge carriers. The bandgap occurs only in samples in which the twist angle between the graphene and hBN crystals is small, resulting in a long-wavelength moiré that acts as a superlattice potential; by adjusting the twist angle the bandgap can be tuned. The moiré superlattice potential also allows us to study the problem of a charged particle in a periodic potential and magnetic field – the so-called Hofstadter problem – whose theoretical solution exhibits a rare instance of fractal behavior in a quantum-mechanical energy spectrum.