Superconductivity and its underlying mechanisms are one of the most active research fields in condensed-matter physics. An important question is how to enhance the transition temperature Tc of a superconductor. In this respect, the possibly positive role of valence-skipping elements in the pairing mechanism has been attracting considerable interest. Here we follow this pathway and successfully enhance Tc up to almost 6 K in the simple chalcogenide SnTe known as a topological crystalline insulator by doping the valence-skipping element In substitutionally for the Sn site and codoping Se for the Te site. A high-pressure synthesis method enabled us to form single-phase solid solutions Sn1-xInxTe1-ySey over a wide composition range while keeping the cubic structure necessary for the superconductivity. Our experimental results are supported by density-functional theory calculations which suggest that even higher Tc values would be possible if the required doping range was experimentally accessible.
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