The effect of pressure and doping on SrPt$_{\mathrm{3}}$P superconductor: First-principles calculations.

Recently, experiments of resistivity and magnetization on SrPt$_{\mathrm{3}}$P under pressure and doping have been conducted by B. Jawdat et al., (Phys.RevB.91,094514(2015)), it was found that with the increase of pressure, the superconducting transition temperature Tc first increases with the maximal at 0.99 Gpa and then decreases, while the Si doping suppress Tc. In this work, we investigate the electronic and phonon properties of SrPt$_{\mathrm{3}}$P under pressure and partial replacement of P by Si, using first-principles method. When pressure increases from 0 to 0.7 Gpa the electron phonon coupling and Tc increases, the calculated Tc agrees with the experiments. For the doped case, SrPt$_{\mathrm{3}}$P$_{\mathrm{0.5}}$ Si$_{\mathrm{0.5}}$ , an additional hole pocket around M point in Brillouin zone is formed, almost all the phonon modes shifts into lower energy, and the density of states at the Fermi level decreases, which may explains the drop in Tc observed experimentally.