Hydrostatic pressure induced three-dimensional Dirac semimetal in black phosphorus

We present the first-principles studies on the hydrostatic pressure effect of the electronic properties of black phosphorus. We show that the energy bands crossover around the critical pressure Pc=1.23 GPa; with increasing pressure, the band reversal occurs at the Z point and evolves into 4 twofold-degenerate Dirac cones around the Z point, suggesting that pressured black phosphorus is a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Γ-Z line move toward the Γ point and evolve into two hole-type Fermi pockets, and those in the Z-M lines move toward the M point and evolve into two tiny electron-type Fermi pockets, and a band above the Z-M line sinks below EF and contributes four electron-type pockets. A clear Lifshitz transition occurs at Pc from semiconductor to 3D Dirac semimetal. Such a 3D Dirac semimetal is protected by the nonsymmorphic space symmetry of bulk black phosphorus. These suggest the bright perspective of black phosphorus for optoelectronic and electronic devices due to its easy modulation by pressure.