Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking

In contrast to conventional Weyl semimetals in achiral crystals, chiral topological semimetals in chiral crystals exhibit Weyl nodes at time-reversal-invariant momenta. A Fermi surface spin texture with parallel spin-momentum locking in these material has been observed by a recent experiment [Nat. Comm. 15,3720(2024)]. We find that the Weyl nodes location and the Fermi surface spin texture lead to gapped zero-momenta intranode superconductivity (SC), which is absent in achiral Weyl semimetals. Through self-consistent mean-field calculations, we find that a cubic lattice system in general favors a mixture of spin-singlet $s_\pm$ and $d+id$-wave pairings. In the presence of only the $s_\pm$-wave pairing, we identify a first-order time-reversal invariant topological SC phase. Notably, an SC phase with two Majorana cones for opened Fermi surfaces is energetically favorable. In addition, a second-order topological superconductor with chiral Majorana states can be realized in the presence of a mixture of $s\pm$- and $d+id$-wave pairing. We show that chiral topological semimetals in cubic lattice are fascinating platforms for exploring intrinsic unconventional superconductivity and topological superconductivity.