Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals

TL;DR

This paper demonstrates that superconducting Dirac and Weyl semimetals can host Majorana zero modes at vortex ends, with the Zeeman field and cone tilting affecting the topological properties.

Contribution

It reveals the conditions under which vortex lines in superconducting Dirac and Weyl semimetals host Majorana zero modes, highlighting the role of Zeeman fields and cone tilting.

Findings

Vortex lines can realize 1D topological superconductivity with Majorana zero modes.

Zeeman fields can open or enhance the topological gap, contrary to previous understanding.

Type-I Dirac and Weyl semimetals have a broader topological regime than type-II.

Abstract

Time-reversal invariant (TRI) Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with $s$-wave pairing and the doping is lower than a critical level, straight $\pi$-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between TRI Dirac and Weyl semimetals and Majorana zero modes in vortices.