Trapping Majorana Quasiparticles with Superconducting Vortices

Topological superconductors are believed to be one of the best venues for achieving non-Abelian Majorana zero modes (MZMs). However, their experimental realization poses considerable challenges. In this talk, I will discuss mechanisms of trapping MZMs with quantum vortices in a topologically trivial s-wave superconductor. I will first describe how normal-state electronic topologies are responsible for various vortex-line topologies in high-Tc iron-based superconductors and further discuss relevant experimental findings. I will then introduce superconducting Luttinger semimetals as a new paradigm for vortex MZMs. If time permits, I will also discuss a computationally efficient approach to numerically evaluate vortex-line topology for real-world superconductors.