Topological Vortices in Superconducting Time-Reversal Symmetric Weyl Semimetals

Recent years have shown that superconducting vortices in topological insulators and strongly spin-orbit coupled semiconductors are natural platforms for obtaining Majorana zero modes. We ask the question, "under what conditions do superconducting vortices in Weyl semimetals trap protected Majorana zero modes on the surface?" We show that sufficient conditions for a time-reversal symmetric type I Weyl semimetal (TWSM) to host Majorana modes as above when ordinary BCS superconductivity is induced in them, are (i) the TWSM forms by perturbing a Dirac or a nodal line semimetal, so that kz=0,pi planes contain pairs of opposite chirality Weyl nodes with a small k-space separation (where z is the vortex axis), and (ii) the number of quadruplets of Weyl nodes in these planes is odd. We analytically calculate the topological invariant in this limit using Kitaev's Pfaffian criterion and support it with numerics on a cubic lattice model. Using our criteria, we predict TaAs and its isovalent counterparts to form topological trivial vortices, devoid of Majorana modes. Also, we propose Na(3-x)KxBi with broken inversion symmetry, where doping occurs via interstitial substitution, to be an ideal platform for realizing a non-trivial superconducting vortex with Majorana zero modes at its ends.