  Based on a combination of $k \cdot p$ theory, band topology analysis and
electronic structure calculations, we predict the (111) thin films of the SnTe
class of three-dimensional (3D) topological crystalline insulators realize the
quantum spin Hall phase in a wide range of thickness. The nontrivial topology
originates from the inter-surface coupling of the topological surface states of
TCI in the 3D limit. The inter-surface coupling changes sign and gives rise to
topological phase transitions as a function of film thickness. Furthermore,
this coupling can be strongly affected by an external electric field, hence the
quantum spin Hall phase can be effectively tuned under experimentally
accessible the electric field. Our results show that (111) thin films of
SnTe-class TCI can be an ideal platform to realize the novel applications of
quantum spin Hall insulators.
