Quasi 1D topological nodal superconducting vortex line state in doped 3D Dirac Semimetals

We study the vortex bound states in three dimensional (3D) Dirac semimetals with both time reversal symmetry and inversion symmetry. Assuming two Dirac points on the kz-axis and bulk s-wave superconductivity, the results turn out to be strongly anisotropic: if the vortex line is perpendicular to the kz-direction, the bulk
superconductor plus a single quantum vortex line is always topologically trivial; if the vortex line is parallel to
the kz-direction, the system has a robust quasi 1D topological nodal superconductor phase, for certain range of
doping level. The emergence of the nodal superconductor phase is a reflection of the topological property of
the Dirac point. Finally, we discuss the possible material realization of such nodal superconducting vortex line
state.