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Superconductors derived from topological insulators and topologicalcrystalline insulators by doping have long been considered to be candidates astopological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topologicalcrystalline insulator with mirror symmetry protected surface states on (001),(011) and (111) oriented surfaces. The superconductor(Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping inPb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Herewe report the first scanning tunneling spectroscopy measurement of thesuperconducting state as well as the superconducting energy gap in(Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te on a (001)-oriented surface. Thespectrum can be well fitted by an anisotropic $s$-wave gap function of$\Delta=0.72+0.18\cos4\theta$ meV using Dynes model. The results show that thequasi-particle density of states seem to be fully gapped without any in-gapstates, in contradiction with the expectation of a topological superconductor.

Fully gapped superconductivity in In-doped topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te