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As a promising candidate system to realize topological superconductivity, thesystem of a 3D topological insulator (TI) grown on top of the s-wavesuperconductor has been extensively studied. To access the topologicalsuperconductivity experimentally, the 3D TI sample must be thin enough to allowfor Cooper pair tunneling to the exposed surface of TI. The use of magneticallyordered dopants to break time-reversal symmetry may allow the surface of a TIto host Majorana fermion, which are believed to be a signature of topologicalsuperconductivity. In this work, we study a magnetically-doped thin filmTI-superconductor hybrid systems. Considering the proximity induced orderparameter in thin film of TI, we analyze the gap closing points of theHamiltonian and draw the phase diagram as a function of relevant parameters:the hybridization gap, Zeeman energy, and chemical potential of the TI system.Our findings provide a useful guide in choosing relevant parameters tofacilitate the observation of topological superconductivity in thin filmTI-superconductor hybrid systems. In addition, we further perform numericalanalysis on a TI proximity coupled to a s-wave superconductor and find that,due to the spin-momentum locked nature of the surface states in TI, the induceds-wave order parameter of the surface states persists even at large magnitudeof the Zeeman energy.

Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor