  Since the advent of topological insulators hosting symmetry-protected Dirac
surface states, efforts have been made to gap these states in a controllable
way. A new route to accomplish this was opened up by the discovery of
topological crystalline insulators (TCIs) where the topological states are
protected by real space crystal symmetries and thus prone to gap formation by
structural changes of the lattice. Here, we show for the first time a
temperature-driven gap opening in Dirac surface states within the TCI phase in
(Pb,Sn)Se. By using angle-resolved photoelectron spectroscopy, the gap
formation and mass acquisition is studied as a function of composition and
temperature. The resulting observations lead to the addition of a temperature-
and composition-dependent boundary between massless and massive Dirac states in
the topological phase diagram for (Pb,Sn)Se (001). Overall, our results
experimentally establish the possibility to tune between a massless and massive
topological state on the surface of a topological system.
