Strain and electric field co-modulation of electronic properties of bilayer boronitrene

The electronic properties of bilayer strained boronitrenes are investigated under an external electric field using density functional methods. Our result is just the same as the previous conclusion: ie, that the electric field will reduce their band gaps. Except for the decrease of their band gaps, the degeneracy of π valence bands at K points will be lifted and the degenerate gap will increase with the electric field increasing. Moreover, the widths of π valence bands are nearly robust and increase a little. In addition, a simple tight-binding model, where different electrostatic potentials are applied to boronitrene layers, can be sufficient to describe the variations of their band gaps. It is found that the interlayer hopping interaction increases while the intralayer hopping parameter changes little with increasing the electric field. Furthermore, a band gap phase diagram is determined within the in-plane strain [-0.2, 0.2] and the interlayer bias [0, 10] V nm(-1). The strain could make the bottom of conduction bands shift from K to M, then to Γ in the Brillouin zone, while the top of valence bands shifts from K to Γ. Thus, a direct-gap semiconductor at K points is changed into an indirect-gap semiconductor, and then a semiconductor with the direct band gap at Γ points. When bilayer boronitrene is a semiconductor with a direct gap at K points, the electric field and strain are inverse proportional relationships. Particularly, when the compressive strain exceeds  -0.194, there is an insulator-metal transition and the system becomes metallic with sizable pocket Fermi surfaces.