  The creation of van der Waals heterostructures based on a graphene monolayer
and other two-dimensional crystals has attracted great interest because atomic
registry of the two-dimensional crystals can modify the electronic spectra and
properties of graphene. Twisted graphene bilayer can be viewed as a special van
der Waals structure composed of two mutual misoriented graphene layers, where
the sublayer graphene not only plays the role of a substrate, but also acts as
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 less than about 3.5o, corresponding to moir\'e-pattern periods D
longer than 4 nm. However, they totally vanish for theta > 5.5o (D < 2.5 nm).
Such a behavior indicates that the continuum models, which capture
moir\'e-pattern periodicity more accurately at small rotation angles, are no
longer applicable at large rotation angles.
