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The creation of van der Waals heterostructures based on a graphene monolayerand other two-dimensional crystals has attracted great interest because atomicregistry of the two-dimensional crystals can modify the electronic spectra andproperties of graphene. Twisted graphene bilayer can be viewed as a special vander Waals structure composed of two mutual misoriented graphene layers, wherethe sublayer graphene not only plays the role of a substrate, but also acts asan equivalent role as the top graphene layer in the structure. Here we reportthe electronic spectra of slightly twisted graphene bilayers studied byscanning tunneling microscopy and spectroscopy. Our experiment demonstratesthat twist-induced van Hove singularities are ubiquitously present for rotationangles theta less than about 3.5o, corresponding to moir\'e-pattern periods Dlonger than 4 nm. However, they totally vanish for theta > 5.5o (D < 2.5 nm).Such a behavior indicates that the continuum models, which capturemoir\'e-pattern periodicity more accurately at small rotation angles, are nolonger applicable at large rotation angles.

Angle-Dependent van Hove Singularities and Their Breakdown in Twisted Graphene Bilayers