  We study topological vortex phases in iron-based superconductors. Besides the
previously known vortex end Majorana zero modes (MZMs) phase stemming from the
existence of a three dimensional (3D) strong topological insulator state, we
show that there is another topologically nontrivial phase as iron-based
superconductors can be doped superconducting 3D weak topological insulators
(WTIs). The vortex bound states in a superconducting 3D WTI exhibit two
different types of quantum states, a robust nodal superconducting phase with
pairs of bulk MZMs and a full-gap topologically nontrivial superconducting
phase which has single vortex end MZM in a certain range of doping level.
Moreover, we predict and summarize various topological phases in iron-based
superconductors, and find that carrier doping and interlayer coupling can drive
systems to have phase transitions between these different topological phases.

Superconductivity