Silicon pseudo-Dirac nodal-sphere semimetal from high-throughput structure screening

Dirac nodal sphere (DNS) semimetals possess unique electronic properties beyond the Dirac nodal points and Dirac nodal lines paradigm. However, Dirac nodal sphere semimetals are very rare in real materials as it is very difficult to realize with discrete crystal point group symmetries. In this work, a silicon structure $({\mathrm{I}4}_{1}/\mathrm{acd}\text{\ensuremath{-}}{\mathrm{Si}}_{80})$ with pseudo-Dirac nodal sphere (PDNS) is proposed via the high-throughput screening for silicon based on our ${\mathrm{RG}}^{2}$ code and transferable tight-binding (TB) method from 2573 silicon allotropes. The results show that the pseudo-Dirac nodal sphere is around the $\mathrm{\ensuremath{\Gamma}}$ point with glide symmetries protected Dirac nodal loops (DNLs) on high-symmetry planes and tiny energy gap $(<1 \mathrm{meV})$ at the general band crossing points. Our calculations of phonon spectrum, $ab$ initio molecular dynamics, elastic constants, and formation energy show that ${\mathrm{I}4}_{1}/\mathrm{acd}\text{\ensuremath{-}}{\mathrm{Si}}_{80}$ is a metastable phase of silicon. Furthermore, ${\mathrm{I}4}_{1}/\mathrm{acd}\text{\ensuremath{-}}{\mathrm{Si}}_{80}$ exhibits interesting photoelectric properties with photoexcitable high-velocity Dirac fermions and has potential applications in Si-based photoelectric devices.