Phase manipulation and Majorana zero modes in iron-based superconductor

Recent experiments reported the evidence of Majorana mode trapped by vortex, crystalline domain wall and magnetic impurity in some iron-based superconductors. For the latter two cases, the underlying physics is not settled down, and the debate is still present. We argue that the phase of superconducting pairing can be manipulated by the ferromagnetism spontaneously formed in the crystalline domain wall and the natively arising in the magnetic impurity. Such phase manipulation plays a crucial role to induce the Majorana mode. Following this line, we show that our theory can be used to understand the experimental signatures about the Majornana mode induced by crystalline domain wall in Fe(Te,Se) and by magnetic impurity in Fe(Te,Se), LiFeAs, monolayer Fe(Te,Se)/SrTiO3 and other iron-based SC platform, and can explain the controversial observations and confusing features of the zero modes from different experiments. We also discuss the some interesting features of the Majorana mode beyond the current experiments and beyond the conventional understandings.