ABSTRACT
The twisted bilayer graphene systems have been successfully generated in experimental laboratories through the various methods, such as, the mechanical exfoliation, the chemical vapor deposition method, and transfer-free method. There exists a relative rotation angle between two honeycomb lattices, being clearly identified from the high-resolution scanning tunneling microscopy measurements. Both scanning tunneling spectroscopy and transport experiments on twisted bilayer graphenes could provide enough information on the low-energy physical properties. On the theoretical progress of twisted bilayer graphene systems, the first-principles method, the effective-mass approximation, and the tight-binding model are available in exploring their essential properties. The bilayer graphene systems, including the normal and twisted stacking configurations, exhibit the rich band structures, mainly owing to the regular/enlarged unit cells and distinct interlayer hopping integrals. The rich electronic energy spectra and wave functions are responsible for the unusual optical properties in the twisted bilayer graphene systems.
