Scanning tunneling microscopy and spectroscopy of finite-size twisted bilayer graphene

Finite-size twisted bilayer graphene (TBG, where here the TBG is of nanoscale size) is quite unstable and will change its structure to a Bernal (or $AB$-stacking) bilayer with a much lower energy. Therefore, the lack of finite-size TBG makes its electronic properties difficult to access in experiments. In this paper, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 to 0 nm. By using scanning tunneling microscopy, we study carefully the structure and the electronic properties of finite-size TBG. Our results indicate that the low-energy electronic properties, including twist-induced Van Hove singularities (VHSs) and spatial modulation of the local density of states, are strongly affected by the translational symmetry breaking of the finite-size TBG. However, the electronic properties above the energy of the VHSs are almost not influenced by quantum confinement even when the width of the TBG is reduced to only a single moir\'e spot.