Multi-band s⁺⁺ superconductivity in V₃Si determined from the response to a controlled disorder

Superfluid density, ρ(T), of a high-quality V₃Si single crystal shows fully-gapped isotropic BCS superconductivity with an additional distinct feature of two almost decoupled superconducting gaps. However, this ρ(T) can be obtained if these two order parameters have different (s_±) or the same (s₊₊) sign. To investigate, the sample was irradiated at 20 K by 2.5 MeV electrons three times, repeating the measurements between the irradiation runs. A large total dose of 6×10¹⁹ cm^-2 was accumulated, after which the superconducting transition temperature, T_c, decreased from 16.4 K in pristine state to 14.7 K. This substantial suppression is impossible for a single isotropic gap, yet it is not large enough for a sign-changing s_±  pairing state. The electronic band structure calculations show how five bands crossing the Fermi level can naturally support two effective gaps, not dissimilar from the iron pnictides. The two-gap self-consistent theories for both, ρ(T) and △T_c, describe the data very well. Thus, the experimental results and theoretical analysis provide strong support for s₊₊ superconductivity with two unequal gaps, △₁ =2.5 meV and △₂ =1.4 meV, and a very weak inter-band coupling in the V₃Si superconductor.