Microscopic characterization of the superconducting gap function in Sn1−xInxTe

Superconductivity in the doped topological crystalline insulator ${\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{Te}$ is studied by first-principles calculation based on superconducting density functional theory (SCDFT) and tunneling spectroscopy. By considering the spin-orbit coupling and frequency dependence of the screened Coulomb interaction in SCDFT, we succeed in reproducing the critical temperature of ${\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{Te}$ quantitatively, in which the spin-orbit coupling is found to play an essential role. The leading gap function is a conventional $s$ wave with moderate anisotropy in $\mathbit{k}$ space, and we find that the subdominant odd-parity instability is significantly weaker than the $s$-wave instability. We perform tunneling spectroscopy measurement and confirm that the spectrum is consistent with the calculated gap function.