Effect of warpage on the electronic structure and optical properties of bilayer germanene

The electronic structure and optical properties of bilayer germanene under different warpages are studied by the first-principles method of density functional theory. The effects of warpages on the electronic structure and optical properties of bilayer germanene are analyzed. The results of the electronic structure study show that the bottom of the conduction band of bilayer germanene moves to the lower energy direction with the increase of warpages at the K point, and the top of the valence band stays constant at the K point, and so the band gap decreases with the increase of warpage. When the warpage is 0.075 nm, the top of the valence band of bilayer germanene changes from K point to G point, and the bilayer germanene becomes an indirect band gap semiconductor. This is an effective means to modulate the conversion of bilayer germanene between direct band gap semiconductor and indirect band gap semiconductor by adjusting the band structure of bilayer germanene effectively. The study of optical properties shows that the effect of warpage on the optical properties of bilayer germanene is mainly distributed in the ultraviolet and visible regions, and the warpage can effectively regulate the electronic structure and optical properties of bilayer germanene. When the warpage is 0.069 nm, the first peak of dielectric function and extinction coefficient is the largest, and the energy corresponding to the absorption band edge is the smallest. Therefore, the electron utilization rate is the best when the warpage is 0.069 nm.