Band structures of Bernal graphene modulated by electric fields

The tight-binding model is utilized to investigate the influence of modulation electric fields on bilayer Bernal graphene (BBG). The electric potential changes the parabolic bands into oscillatory ones, and induces more band-edge states. As the strength of field is strengthened, it would enhance the oscillation of energy band, affect larger range of energy, induced more band-edge states, and cause more overlapping of valence and conduction band. While the period of field is enhanced, the number of sub-bands and band-edge states would increase. However the deformation of energy band is less violent. The essential features of electronic structure are directly reflected on the density of states (DOS). DOS displays many prominent peaks resulting from the induced band-edge states.