Topological crystalline insulators (TCIs) are a new class of topological materials that possess unique metallic surface states protected by crystalline mirror symmetry. Their topological surface properties are expected to strongly depend on the surface orientation. By combining density functional theory (DFT) calculations and synthesis experiments, we demonstrate the controlled growth of single crystalline nanostructures of the prototypical TCI SnTe with distinct facets and morphologies. Our calculations suggest that the excess energy of the {111} surfaces can be either higher or lower than that of the {100} surfaces, depending on the stoichiometry, while the {110} is always higher than the {100}. In our synthesis experiment, we qualitatively controlled the stoichiometry by tailoring the growth temperature and obtained two types of single crystalline nanowires: smooth nanowires dominated by {100} facets at high temperatures and zigzag nanowires composed of both {100} and {111} surfaces at low temperatures. Notably, there is no {110} facet in our nanostructures, strongly supporting the DFT calculations. Our device fabrication and electrical characterizations suggest that both types of nanowires are suitable for transport studies of topological surface states.

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