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Recent experiment reported the evidence of dispersing one-dimensionalMajorana mode trapped by the crystalline domain walls inFeSe$_{0.45}$Te$_{0.55}$. Here, we perform the first-principles calculations toshow that iron atoms in the domain wall spontaneously form the ferromagneticorder in line with orientation of the wall. The ferromagnetism can impose a$\pi$ phase difference between the domain-wall-separated surfacesuperconducting regimes under the appropriate width and magnetization of thewall. Accordingly, the topological surface superconducting state ofFeSe$_{0.45}$Te$_{0.55}$ can give rise to one-dimensional Majorana modestrapped by the wall. More interestingly, we further propose a surface junctionin the form of FeSe$_{0.45}$Te$_{0.55}$/ferromagnet/FeSe$_{0.45}$Te$_{0.55}$,which can be adopted to create and fuse the Majorana zero modes throughcontrolling the width or magnetization of the interior ferromagnetic barrier.The braiding and readout of Majorana zero modes can be realized by the designeddevice. Such surface junction has the potential application in thesuperconducting topological quantum computation.

Phase-manipulation-induced Majorana Mode and Braiding Realization in Iron-based Superconductor Fe(Te,Se)