2D selenium allotropes from first principles and swarm intelligence.

Combining the particle-swarm optimization method with first-principles calculations, we explore a new category of two-dimensional (2D) monolayers composed of solely the element selenium. Three stable structures are screened from outputs of crystal search computations, namely T-Se (1T-MoS-like), C-Se (tiled 1D helical chain), and S-Se (square structure). Phonon calculations, as well as formation energy calculations have been performed to confirm the stability of the three phases. The electronic structure calculations show that both T-Se and C-Se are indirect-band-gap semiconductors, with gap values of 1.11 eV and 2.64 eV respectively when using the hybrid HSE06 functional. In particular, C-Se has a centrosymmetry-breaking structure which provides a spontaneous in-plane ferroelectric polarization of about 2.68  ×  10 C m per layer. Interestingly, S-Se has a Dirac cone that can open up a band gap of 0.11 eV if spin-orbit coupling is included. The tilted Dirac cone of S-Se shows anisotropic band dispersion as characterized with different Fermi velocities of 1.26  ×  10 and 0.24  ×  10 m s around the Dirac point. Our works enrich the family of 2D materials of selenium allotropes and show that their versatile properties could give rise to potential application in various fields.