In this Letter we report on proximity superconductivity induced in CdTe-HgTe core-shell nanowires, a quasi-one-dimensional heterostructure of the topological insulator HgTe. We demonstrate a Josephson supercurrent in our nanowires contacted with superconducting Al leads. The observation of a sizable I R product, a positive excess current, and multiple Andreev reflections up to fourth order further indicate a high interface quality of the junctions.
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