Topological Superconductivity in Multifold Fermion Metals.

Recently, two multifold fermions materials, AlPt[arXiv:1812.03310] and XSi(X=Rh,Co)[arXiv:1812.04466][arXiv:1901.03358][arXiv:1809.01312], characterized by multifold degeneracy band crossings at time-reversal invariant momenta (TRIMs) have been discovered in chiral crystals experimentally. In this work, we largely expand the family of multifold fermions by pointing out that several well-studied noncentrosymmetric superconductors are indeed multifold fermion metals. Importantly, their normal state topological properties, which have been ignored in previous studies, play an important role in the superconducting properties. Taking Li$_2$Pd$_3$B and Li$_2$Pt$_3$B as examples, we found a large number of unconventional degenerate point, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in Li$_2$Pd$_3$B, originating from the nontrivial band topology were found. Importantly, it has been shown experimentally that Li$_2$Pd$_3$B and Li$_2$Pt$_3$B are fully gapped and gapless superconductors respectively. By analyzing the possible pairing symmetries, we suggest that Li$_2$Pd$_3$B can be a DIII class topological superconductor with Majorana surface states, even if the spin-orbit coupling in Li$_2$Pd$_3$B is negligible. Interestingly, Li$_2$Pt$_3$B, being gapless, is likely to be a nodal topological superconductor with dispersion-less surface Majorana modes. We further identified that several noncentrosymmetric superconductors, such as Mo$_3$Al$_2$C, PdBiSe, Y$_2$C$_3$ and La$_2$C$_3$, are multifold fermion superconductors whose normal state topological properties have been ignored in previous experimental and theoretical studies.