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We study a vortex chain in a thin film of a topological insulator withproximity-induced superconductivity---a promising platform to realize Majoranazero modes (MZMs)---by modeling it as a two-leg Majorana ladder. While eachpair of MZMs hybridizes through vortex tunneling, we hereby show that MZMs canbe stabilized on the ends of the ladder with the presence of tilted externalmagnetic field and four-Majorana interaction. Furthermore, a fruitful phasediagram is obtained by controlling the direction of magnetic field and thethickness of the sample. We reveal many-body Majorana states andinteraction-induced topological phase transitions and also identifytrivial-superconducting and commensurate/incommensurate charge-density-wavestates in the phase diagram.

Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure