Multiple Pairs of Propagating Majorana Modes in the Votex Line of Superconducting Quadratic Dirac Semimetals

We study the vortex bound states in a class of three dimensional (3D) time reversal invariant quadratic Dirac semimetals. Assuming intrinsic s-wave superconductivity, we find that multiple Majorana modes can be bound to the vortex line for certain range of doping level. Specifically, due to the quadratic Dirac points in the band structures, quasi-1D Majorana modes carrying angular momentum ±1 and ±2 can propagate along the vortex line; for quadratic Dirac semimetals with nontrival Z2 topological character, additional 0D Majorana zero modes carrying angular momentum 0 can be bound at the end of the vortex line. Together with our work in linear Dirac semimetals (Phys. Rev. Lett. 123, 027003), we establish a complete correspondence between the topological properties of the normal state band structures and the vortex bound states in the s-wave superconducting state.