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Using scanning tunnel microscopy (STM), we investigate the superconductivityand vortex properties in topological insulator Bi$_{2}$Te$_{3}$ thin filmsgrown on the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$. Theproximity-induced superconductivity weakens in the Bi$_{2}$Te$_{3}$ film whenthe thickness of the film increases. Unlike the elongated shape of vortex coresobserved in the Bi$_{2}$Te$_{3}$ film with 2-quintuple-layer (QL) thickness,the isolated vortex cores exhibit a star shape with six rays in the 1-QL film,and the rays are along the crystalline axes of the film. This is consistentwith the sixfold rotational symmetry of the film lattice, and theproximity-induced superconductivity is still topologically trivial in the 1-QLfilm. At a high magnetic field, when the direction between the two nearestneighbored vortices deviates from that of any crystalline axes, two coresconnect each other by a pair of adjacent rays, forming a new type of electronicstructure of vortex cores. On the 3-QL film, the vortex cores elongate alongone of the crystalline axes of the Bi$_{2}$Te$_{3}$ film, similar to theresults obtained on 2-QL films. The elongated vortex cores indicate a twofoldsymmetry of the superconducting gap induced by topological superconductivitywith odd parity. This observation confirms possible topologicalsuperconductivity in heterostructures with a thickness of more than 2 QLs. Ourresults provide rich information for the vortex cores and vortex-bound stateson the heterostructures consisting of the topological insulator and theiron-based superconductor.

physical review. b./physical review. b

Superconductivity and vortex structure on  Bi$_{2}$Te$_{3}$/FeTe$_{0.55}$Se$_{0.45}$ heterostructures with different  thickness of Bi$_{2}$Te$_{3}$ films