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 twofolddegenerate 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 2 hole-type Fermi pockets, and those in the Z-M lines move toward the M point and evolve into 2 tiny electron-type Fermi pockets, and a band above the Z-M line sinks below EF and contributes 4 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.
I. MOTIVATIONSThe van der Waals force between layers makes layered compounds graphite, MoS 2 , WTe 2 and TaS 2 , etc.,be easily exfoliated to monolayers as two-dimensional materials, such as graphite to graphene and MoS 2 to its monolayer. As a possible candidate of optoelectronic and electronic material, the energy gap of black phosphorus varies from 0.3 eV in bulk to about 2 eV in monolayer, filling the optical interval between small energy gap 0-0.3 eV in graphene and large energy gap of 1-2 eV in semiconductive dichalcogenides [1]. Recently, black phosphorus in bulk, multilayers and monolayers have received considerable interests [2][3][4]. Zhang et al. demonstrated that multilayer black phosphorus exhibits as high as 10 5 drain current modulation and 10 3 cm 2 V −1 s −1 charge mobility [5], showing that black phosphorus thin film might be a good potential candidate for field effect transistor [6]. More recently it is shown that a moderate hydrostatic pressure could not only drive semiconductive black phosphorus to metallic, but also tune multiple Fermi surfaces and Lifshitz point in the magnetotransport and ShubnikovDe Haas oscillation measurements [7]. These properties make black phosphorus a new exciting field both in material sciences and condensed matter physics [8].Hydrostatic pressure could easily change the crystal structure of black phosphorus and modify its electronic properties [3,9]. As the most stable allotrope of phosphorus, black phosphorus exhibits three different phases under moderate high hydrostatic pressures: the orthorhombic phase with wrinkled hexagons, the graphene-like rhombohedral phase with hexagonal lattice for the pressure P >4.5 GP a [10], and the simple cubic phase for P >10.3 GP a [10]. Under high pressure the P-P bond lengths and bond angle of black phosphorus display strong pressure dependence, and exhibit highly anisotropy in compressibility [9]. Though a strain may crucially modify the energy gap of monolayer black phosphorus [3], it is com...