  Topological crystalline insulators are new states of matter in which the
topological nature of electronic structures arises from crystal symmetries.
Here we predict the first material realization of topological crystalline
insulator in the semiconductor SnTe, by identifying its nonzero topological
index. We predict that as a manifestation of this nontrivial topology, SnTe has
metallic surface states with an even number of Dirac cones on high-symmetry
crystal surfaces such as {001}, {110} and {111}. These surface states form a
new type of high-mobility chiral electron gas, which is robust against disorder
and topologically protected by reflection symmetry of the crystal with respect
to {110} mirror plane. Breaking this mirror symmetry via elastic strain
engineering or applying an in-plane magnetic field can open up a continuously
tunable band gap on the surface, which may lead to wide-ranging applications in
thermoelectrics, infrared detection, and tunable electronics. Closely related
semiconductors PbTe and PbSe also become topological crystalline insulators
after band inversion by pressure, strain and alloying.
