Graphene Bilayer with a Twist: Electronic Structure

We consider a graphene bilayer with a relative small angle rotation between the layers—a stacking defect often seen in the surface of graphite—and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in an 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.