  Topological crystalline insulators (TCI) are unique systems where a band
inversion that is protected by crystalline mirror symmetry leads to a
multiplicity of topological surface states. Binary SnTe is an attractive
lead-free TCI compound; the present work on high-quality thin films provides a
route for increasing the mobility and reducing the carrier density of SnTe
without chemical doping. Results of quantum coherent magnetotransport
measurements reveal a multiplicity of Dirac surface states that are unique to
TCI. Modeling of the weak antilocalization shows variations in the extracted
number of carrier valleys that reflect the role of coherent intervalley
scattering in coupling different Dirac states on the degenerate TCI surface.
