Semiconductor-to-metal transition from monolayer to bilayer blue phosphorous induced by extremely strong interlayer coupling: a first-principles study

Monolayer blue phosphorous has a large band gap of 2.76 eV but counterintuitively the most stable bilayer blue phosphorous has a negative band gap of -0.51 eV. Such a large band gap reduction from just monolayer to bilayer has not been revealed before, the underlying mechanism behind which is important for understanding interlayer interactions. In this work, we reveal the origin of the semiconductor-to-metal transition using first-principles calculations and tight-binding models. We find that the interlayer interactions are extremely strong, which can be attributed to the short layer distance and strong π-like atomic orbital couplings. Therefore, the upshift of the valence band maximum (VBM) from monolayer to bilayer blue-P is so large that the VBM in the bilayer gets higher than the conduction band minimum, leading to a negative band gap and an energy gain. Besides, the interlayer atomic misplacements weaken the couplings of out-of-plane orbitals. Therefore, the energy gain due to the semiconductor-to-metal transition is larger than the energy cost due to interlayer repulsions, thus stabilizing the metallic phase. The large band gap reduction with layer number increasing is expected to exist in other similar layered systems.