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Electronic Structures and Their Landau Quantizations in Twisted Graphene Bilayer and Trilayer

Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monolayer. Our result demonstrates that both the VHSs and Fermi velocity of the twisted bilayer depends remarkably on the twist angle and the interlayer coupling strength. In the twisted trilayer, we directly observe Landau quantization of massive Dirac fermion with a sizable band gap 105 meV, which results in valley (layer) polarization of the lowest Landau levels. Such a result is similar to the expected Landau quantization in Bernal graphene bilayer with a moderate electric field.