We report molecular beam epitaxial growth of a SnTe (111) layer on a CdTe template, fabricated by depositing it on a GaAs (111)A substrate, instead of BaF$_2$ which has been conventionally used as a substrate. By optimizing temperatures for the growth of both SnTe and CdTe layers, we could obtain SnTe layers of the single phase grown only in the (111) orientation and of much improved surface morphology from the viewpoint of the extension and the flatness of flat regions, compared to the layers grown on BaF$_2$. In this optimal growth condition, we have also achieved a low hole density of the order of 10$^{17}$cm$^{-3}$ at 4K, the lowest value ever reported for SnTe thin films without additional doping. In the magnetoresistance measurement on this optimized SnTe layer, we observe characteristic negative magneto-conductance which is attributed to the weak antilocalization effect of the two-dimensional transport in the topological surface state.
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