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-MoS₂-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  ×  10⁻¹⁰ C m⁻¹ 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  ×  10⁶ and 0.24  ×  10⁶ m s⁻¹ 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. (paper)