Superconductivity induced by In substitution into the topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te

Indium substitution turns the topological crystalline insulator (TCI) Pb$_{0.5}$Sn$_{0.5}$Te into a possible topological superconductor. To investigate the effect of the indium concentration on the crystal structure and superconducting properties of (Pb$_{0.5}$Sn$_{0.5}$)$_{\mathrm{1-x}}$In$_{\mathrm{x}}$Te, we have grown high-quality single crystals using a modified floating-zone method and have performed systematic studies for indium content in the range 0 $\le $ x $\le $ 0.35. We find that the single crystals retain the rocksalt structure up to the solubility limit of indium (x $\sim $ 0.30). Experimental dependencies of the superconducting transition temperature (T$_{\mathrm{c}})$ and the upper critical magnetic field (H$_{\mathrm{c2}})$ on the indium content x have been measured. The maximum T$_{\mathrm{c}}$ is determined to be 4.7 K at x $=$ 0.30, with $\mu_{\mathrm{0}}$H$_{\mathrm{c2}}$(T $=$0) $\approx $ 5T.