Angle Dependent Van Hove Singularities in 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 (DOS) could be induced in twisted graphene bilayer. Here, we report angle dependent VHSs of slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows \DeltaEvhs ~ \hbar{\nu}F\DeltaK between 1.0^{\circ} and 3.0^{\circ} (here {\nu}F ~ 1.1\times106 m/s is the Fermi velocity of monolayer graphene, \DeltaK = 2Ksin(\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 not results in significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle \theta ~ 1.3^{\circ}, the observed \DeltaEvhs ~ 0.11 eV is much less than the expected value \hbar{\nu}F\DeltaK ~ 0.28 eV at 1.3^{\circ}. The origin of the reduction of \DeltaEvhs at 1.3^{\circ} is discussed.