Superconducting topological Dirac semimetals: P6/m−Si6 and P6/m−NaSi6

We theoretically propose that hexagonal silicon-based crystals $P6/m\text{\ensuremath{-}}{\mathrm{Si}}₆$ and $P6/m\text{\ensuremath{-}}{\mathrm{NaSi}}₆$ are topological Dirac semimetals with superconducting critical temperatures of 12 K and 13 K, respectively, at ambient pressure. Band inversion occurs with the Fu-Kane topological invariant ${\mathbb{Z}}₂=1$, even in the absence of spin-orbit coupling. The Dirac nodes protected by ${C}₆$ crystal rotational symmetry remain gapless with spin-orbit coupling. Using first-principles calculations, we find pressure-induced topological phase transitions for $P6/m\text{\ensuremath{-}}{\mathrm{Si}}₆$ and $P6/m\text{\ensuremath{-}}{\mathrm{NaSi}}₆$ with critical external pressures of 11.5 GPa and 14.9 GPa, respectively. Above the critical pressures, the Dirac bands are gapped with ${\mathbb{Z}}₂=0$, while the superconducting states and the crystal symmetries are retained. Our results may shed light into a search for silicon-based topological materials with superconductivity.