Modulation Effects of Periodic Potentials on the Electronic Properties of Bilayer Bernal Graphene: Tight-Binding Model

Abstract

Electronic properties of bilayer Bernal graphene under modulated electric fields are calculated by the tight-binding model with an exact diagonalization method. This approach efficiently calculates the energy bands, wave functions and densities of states (DOS). Such electronic properties are highly correlated to the strength, period and direction of the electric field. The interlayer atomic interactions result in two groups of subbands, and these subbands are significantly influenced by the electric fields, such as altered energy dispersions, strengthened overlapping, broken degeneracy, and a great amount of induced band-edge states. The electric fields also change main features of the wave functions, including the number of zero points, distribution symmetry, and standing-wave-like feature. The DOS at the Fermi energy rises with the growing field strength, but is not susceptible to the field period. Furthermore, the electric fields reveal different impacts on the two groups of subbands.