Competing Vortex Topologies in Iron-based Superconductors

In this work, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (tFeSCs). While tFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic $s$-wave superconductivity, our theory implies that such common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for tFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in tFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for tFeSCs and is directly relevant to tFeSC candidates such as LiFeAs.When the four-fold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana-free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. Origin of Majorana signal in other tFeSC candidates such as FeTe$_x$Se$_{1-x}$ and CaKFe$_4$As$_4$ are also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.