We have identified a two-dimensional (2D) beryllium diphosphide (${\mathrm{BeP}}_2$) structure using a global structure search combined with first-principles calculations. Phonon calculations and molecular dynamics simulation confirm that the structure is dynamically and thermally stable. Electronic structure calculations show that the 2D sheet is a direct band gap semiconductor with a small band gap of 0.15 eV, and the intrinsic acoustic-phonon-limited carrier mobility of the structure can reach $\sim {10}^4{\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ for both electrons and holes with anisotropic features in the $x$ and $y$ directions. More interestingly, both mechanical and chemical compression can close the band gap and the structure turns to a Dirac semimetal with the Dirac cones located exactly at the Fermi level. The emerged Dirac semimetal state is direction dependent, with a linear band dispersion in the $x$ direction and a quadratic one in the $y$ direction. Moreover, it is demonstrated that the Dirac point is symmetry protected in the absence of spin-orbit coupling (SOC). In ${\mathrm{BeP}}_2$, the SOC is too weak to alter the semimetal feature except for the cases at extremely low temperatures. The band gap closing mechanism is further clarified by using the tight-binding (TB) method.

• Received 25 August 2017
• Revised 9 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.085418