  Discovery of topologically protected surface states, believed to be immune to
weak disorder and thermal effects, opened up a new avenue to reveal exotic
fundamental science and advanced technology. While time-reversal symmetry plays
the key role in most such materials, the bulk crystalline symmetries such as
mirror symmetry preserve the topological properties of topological crystalline
insulators (TCIs). It is apparent that any structural change may alter the
topological properties of TCIs. To investigate this relatively unexplored
landscape, we study the temperature evolution of the Dirac fermion states in an
archetypical mirror-symmetry protected TCI, SnTe employing high-resolution
angle-resolved photoemission spectroscopy and density functional theory
studies. Experimental results reveal a perplexing scenario; the bulk bands
observed at 22 K move nearer to the Fermi level at 60 K and again shift back to
higher binding energies at 120 K. The slope of the surface Dirac bands at 22 K
becomes smaller at 60 K and changes back to a larger value at 120 K. Our
results from the first-principles calculations suggest that these anomalies can
be attributed to the evolution of the hybridization physics with complex
structural changes induced by temperature. In addition, we discover drastically
reduced intensity of the Dirac states at the Fermi level at high temperatures
may be due to complex evolution of anharmonicity, strain, etc. These results
address robustness of the topologically protected surface states due to thermal
effects and emphasize importance of covalency and anharmonicity in the
topological properties of such emerging quantum materials.
