Angle-dependent van Hove singularities and their breakdown in twisted graphene bilayers

The creation of van der Waals heterostructures based on a graphene monolayer and other two-dimensional crystals has attracted great interest because the atomic registry of the two-dimensional crystals can modify the electronic spectra and properties of graphene. A twisted graphene bilayer can be viewed as a special van der Waals structure composed of two mutually misoriented graphene layers, where the sublayer graphene not only plays the role of a substrate, but also acts in an equivalent role as the top graphene layer in the structure. Here we report the electronic spectra of slightly twisted graphene bilayers studied by scanning tunneling microscopy and spectroscopy. Our experiment demonstrates that twist-induced van Hove singularities are ubiquitously present for rotation angles [theta] of less than about 3.5[degrees], corresponding to moire-pattern periods D longer than 4 nm. However, they totally vanish for [theta]>5.5[degrees] (D < 2.5nm). Such a behavior indicates that the continuum models, which capture moire-pattern periodicity more accurately at small rotation angles, are no longer applicable at large rotation angles.