Double Majorana vortex flat bands in the topological Dirac superconductor

Vortex lines, known as topological defects, are capable of trapping Majorana modes in superconducting topological materials. Previous studies have primarily focused on topological bands with conventional s-wave pairing. However, topological Dirac semimetals exhibiting a unique orbital texture can favor unconventional pairing when electronic correlations are significant. The topology of vortices in these systems remains elusive and unexplored. In this work, we investigate the vortex bound states in C4z-symmetric superconducting Dirac semimetals, with a particular focus on the orbital-singlet unconventional pairing, which generates higher-order Majorana hinge modes. We identify robust doubly-degenerate Majorana vortex flat bands at zero energy in both type-I and type-II Dirac semimetals. These doubly-degenerate flat bands arise from a nontrivial $${{\mathbb{Z}}}_{2}$$ topology defined by an effective particle-hole symmetry and are protected by the four-fold rotational symmetry. Additionally, we observe that moving the vortex line close to a hinge can trivialize the higher-order Majorana arc on the hinge, leaving a single Majorana mode at the vortex core due to the hybridization of Majorana modes. Finally, we discuss the potential experimental implications for correlated Dirac semimetals, such as electron-doped iron-based superconductors. In strongly correlated Dirac semimetals, orbital-singlet, spin-triplet superconducting pairing becomes possible. In this work, the authors predict doubly robust Majorana flat bands bound to the vortex line: confined between the projected nodes in type-I Dirac semimetals and spanning the entire one-dimensional Brillouin zone in type-II Dirac semimetals.