Influence of Fermi Surface Topology on Superconductivity in High-Pressure Phases of Silane

Both a semimetallic molecular phase with P2$_{1}$/m symmetry and a metallic atomic phase with P2$_{1}$/c symmetry are found using \textit{ab initio} geometry optimization method from initial configurations of random molecular SiH$_{4}$ and atoms Si and H, respectively. The molecular phase shows a pressure-induced metallization, which can be described quantitatively by Fermi surface (FS) filling constant defined in our work. The lower superconducting critical temperature (\textit{Tc}) about 16.2 K at 175 GPa and its peculiar superconductive behavior that its \textit{Tc} decreases initially and increases later with pressure agree with a recent experimental results. Different electron-phonon coupling mechanisms are uncovered during the increase and decrease of \textit{Tc} with pressure. The atomic phase shows a higher Tc of about 47 K at 190GPa and its \textit{Tc} increases with pressure in its dynamically stable range. The FS filling constant and FS topology transitions under pressure mostly account for the different superconductivity between the molecular and atomic phases.