Recent band-structure calculations predicted that the ruthenium-based ternary silicides are three-dimensional Kramers nodal-line semimetals. Among them, NbRuSi and TaRuSi show bulk superconductivity (SC) below $T_c\sim 3\mathrm{K}$ and 4 K, as well as spontaneous magnetic fields. The latter indicate the breaking of time-reversal symmetry and, thus, unconventional SC in both compounds. Previous temperature-dependent muon-spin spectroscopy studies failed to distinguish whether such compounds exhibit single-gap or multigap SC. Here we report on systematic measurements of the field-dependent muon-spin relaxation rates in the superconducting state and on temperature-dependent electrical resistivity and specific heat under applied magnetic fields. Both the upper critical field and the field-dependent superconducting relaxation are well described by a two-band model. By combining our experimental results with numerical band-structure calculations, we provide solid evidence for multiband SC in NbRuSi and TaRuSi, and thus offer further insight into the unconventional and topological nature of their superconductivity.

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• Superconductivity
• Nodal-line semimetals
• Unconventional superconductors
• Density functional theory
• Muon spin relaxation & rotation