Majorana bound states in vortex lattices on iron-based superconductors

Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximity coupled to a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor FeTe(0.55)Se(0.45). In this talk, I will present our recent work on vortex lattices that form in such materials, specifically discussing the emergence of Majorana vortex modes in the presence of magnetic field strength and vortex lattice disorder. I will introduce the technique of singular gauge transformation that we use for modelling vortex lattices under periodic boundary conditions that are normally forbidden. This approach allows us to go to larger vortex lattices that are otherwise inaccessible and is successful in replicating several experimental observations of Majorana vortex bound states in the FeTe(0.55)Se(0.45) platform. Our results can be related to a disordered Majorana lattice model that can be useful for further investigations on the role of interactions, and towards topological quantum computation.