Graphene bilayer with a twist: electronic structure

Understand

Electronic properties of bilayer and multilayer graphene have generally been interpreted in terms of AB or Bernal stacking.

• However, it is known that many types of stacking defects can occur in natural and synthetic graphite; rotation of the top layer is often seen in scanning tunneling microscopy (STM) studies of graphite.
• In this paper we consider a graphene bilayer with a relative small angle rotation between the layers and calculate the electronic structure near zero energy in a continuum approximation.
• Contrary to what happens in a AB stacked bilayer and in accord with observations in epitaxial graphene we find: (a) the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single layer value; (b) an external electric field, perpendicular to the layers, does not open an electronic gap