Singularities and topologically protected states in twisted bilayer graphene

We have studied the structural and electronic properties of twisted bilayer graphene by scanning tunneling microscopy (STM). For twist angles in the range of about 1 degrees to 4 degrees, the twisted bilayer graphene possesses two Van Hove singularities in the vicinity of the Fermi level. We use the exact location of these Van Hove singularities to determine the twist angle dependent interlayer hopping energy. For a twist angle of 0.6 degrees, we found a hexagonal network of topologically protected one-dimensional channels that run along the boundaries of the AB/BA domains. The electric field in the tunnel junction is responsible for the breaking of the symmetry of the AB and BA domains and the development of the hexagonal network of topologically protected states. The latter shows that the electric field in the tunneling junction can significantly affect the topological nature of two-dimensional materials, and therefore, one should be cautious when interpreting scanning tunneling microscopy and spectroscopy experiments of this class of materials.