TaOsSi has been identified as a material with both topological surface states and signatures of unconventional superconductivity, while at the same time showing indications of two-gap superconductivity. We report investigation of electronic and superconducting properties of TaOsSi and the related superconductor NbOsSi based on electron-phonon coupling. We find that these materials are not near magnetism, which implies that spin-fluctuation pairing is unlikely to be operative. There is a momentum-dependent electron-phonon coupling on a multisheet Fermi surface leading to a superconducting state with a highly anisotropic gap in the clean limit. The state is fully gapped in accord with experimental results. We do not find a conventional two-gap state but rather a continuous variation of the gap on the Fermi surfaces. Thus, it is possible to explain the occurrence of superconductivity in these compounds within a conventional electron-phonon picture. Both NbOsSi and TaOsSi show a Dirac point very close to the Fermi energy, $E_F$, along the X-S line near the $S$ point. In the case of NbOsSi, this is 16 meV below $E_F$ at k = (0.5,0.48,0) and in TaOsSi it is 23 meV below $E_F$ at k = (0.5,0.46,0). Thus, these materials are superconductors with strong spin orbit, topological superconductivity, and substantial anisotropy of the superconducting order parameter.

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• First-principles calculations
• Multiband superconductivity
• Pairing mechanisms
• Phonons
• Superconducting gap
• Superconductivity