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$_{0.5}$)$_{1-x}$In$_{x}$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 $0leq xleq 0.35$. We find that the single crystals retain the rock salt structure up to the solubility limit of indium ($xsim0.30$). Experimental dependences of the superconducting transition temperature ($T_c$) and the upper critical magnetic field ($H_{c2}$) on the indium content $x$ have been measured. The maximum $T_c$ is determined to be 4.7 K at $x=0.30$, with $mu_0H_{c2}(T=0)approx 5$ T.
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