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

We study the vortex bound states in three dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. Assuming two Dirac points on the kz-axis and bulk s-wave superconductivity, with a quantum vortex line parallel to the z-direction, we find that the superconducting vortex line has a robust quasi-1D nodal phase. The nodal phase stems from the symmetry protected Dirac points in the normal state bands, and it can be characterized by a topological index (\nu; n) at kz = 0 and kz = \pi, where \nu is the Z2 topological invariant for a 0D class-D system and n is the Z topological invariant for a 0D class-A system according to the Altland- Zirnbauer classification. Based on the topological index, we find that vortex end Majorana zero mode can coexist with the quasi-1D nodal phase in certain kinds of Dirac semimetals. The influence of the symmetry breaking perturbations on the quasi-1D nodal phase is also analyzed. Finally, we discuss the possible material realization of such nodal vortex line state.