Intertwining Josephson and Vortex Topologies in Conventional Superconductors

Topological superconductors are often considered the best venue for non-Abelian Majorana zero modes (MZMs), while their experimental realizations are generally challenging for various reasons. Here, we will discuss two alternative mechanisms for MZMs in a topologically trivial s-wave superconductor, involving a field-induced 1D vortex line and a 2D π-phase Josephson junction. Remarkably, we find that the emergent topological physics of vortex and π-junction are generally intertwined, i.e., they appear under the same material conditions, revealing a new topological correspondence relation between 2D π-junctions and 1D vortex lines. Based on this theoretical finding, we focus on 2M-phase WS₂, a recently synthesized superconductor with electronic Dirac surface state. While experimental evidence of vortex MZMs has been reported for this compound, there has been no theoretical effort to justify the claim due to the computational challenges of simulating a full-size superconducting vortex. We fill in this blank by conducting ab-initio-based π-junction simulations for 2M-WS₂. A nontrivial Josephson topology is found, further predicting the existence of vortex MZM under experimental conditions. We also predict the non-trivial vortex line topology in superconducting Dirac semimetal Sr₃SnO by utilizing this correspondence. Our theory opens a new avenue for searching vortex MZMs in real-world superconductors.