  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 $0\leq x\leq
0.35$. We find that the single crystals retain the rock salt structure up to
the solubility limit of indium ($x\sim0.30$). 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.
