Topological Vortex Phase Transitions in Iron-Based Superconductors

We study topological vortex phases in iron-based superconductors. Besides previously known Majorana zero mode(MZM) phase
protected by the existence of a three dimensional(3D) strong topological insulator(TI), we show that there are two additional phases as iron-based superconductors can be doped superconducting 3D weak topological insulators(3DWTI), a series of two dimensional (2D) topological insulators sticked along the third direction weakly. The vortex bound states of a superconducting 3DWTI, unlike in a 3D strong topological insulator, exhibit two different types of quantum states: (1) a robust nodal superconducting phase with pairs of bulk Majorana zero modes; (2) a full-gap topologically nontrivial superconducting phase, which has single vortex end MZM in a certain range of doping level. The recently observed zero bias peak in the vortex of (Li$_{0.8}$Fe$_{0.2}$)OHFeSe belongs to the second case. We predict that some iron-based superconductors can be 3DWTIs of the first case, namely, their vortex states are quasi one-dimensional topological nodal superconductors.