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

## TL;DR

This paper investigates the topological properties of vortex lines in doped 3D Dirac semimetals with superconductivity, revealing a robust quasi-1D nodal phase protected by symmetry and its potential to host Majorana zero modes.

## Contribution

It introduces the concept of a quasi-1D topological nodal vortex line phase in doped superconducting Dirac semimetals, characterized by specific topological invariants and coexistence with Majorana zero modes.

## Key findings

- Vortex lines exhibit a robust quasi-1D nodal phase protected by symmetry.
- Topological invariants (
u; n) characterize the phase at kz=0 and kz=.
- Majorana zero modes can coexist with the nodal phase in certain materials.

## Abstract

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.