Discovery of exotic phases of matter from the topologically non-trivial systems not only makes the research on topological materials more interesting but also enriches our understanding of the fascinating physics of such materials. Pb$_{0.6}$Sn$_{0.4}$Te was recently shown to be a topological crystalline insulator. Here we show that by forming a mesoscopic point-contact using a normal non-superconducting elemental metal on the surface of Pb$_{0.6}$Sn$_{0.4}$Te a novel superconducting phase is created locally in a confined region under the point-contact. This happens while the bulk of the sample remains to be non-superconducting and the superconducting phase emerges as a nano-droplet under the point-contact. The superconducting phase shows a high transition temperature $T_c$ that varies for different point-contacts and falls in a range between 3.7 K and 6.5 K. Therefore, this Letter presents the discovery of a new superconducting phase on the surface of a topological crystalline insulator and the discovery is expected to shed light on the mechanism of induced superconductivity in topologically non-trivial systems in general.
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