Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer

Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows Delta E-vhs similar to (h) over bar nu(F)Delta K between 1.0 degrees and 3.0 degrees [here nu(F) similar to 1.1 x 10(6) m/s is the Fermi velocity of monolayer graphene, and Delta K = 2K sin(theta/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle theta similar to 1.3 degrees, the observed Delta E-vhs similar to 0.11 eV is much smaller than the expected value (h) over bar nu(F)Delta K similar to 0.28 eV at 1.3 degrees. The origin of the reduction of Delta E-vhs at 1.3 degrees is discussed.