  In this report, we identify the origin of the temperature dependence of the
surface energy gap in impurity-doped topological insulators. The gap at the
Dirac point and its variation with temperature were studied by using
angle-resolved photoemission spectroscopy in Cr-doped Bi2Se3. Our valence band
photoemission results revealed that the gap varies with temperature due to
residual gas condensation on the sample surface with cooling. Adsorbate on the
surface of the sample creates an electron doping effect that modifies the
chemical potential of the system resulting in the change of the gap with
variable temperature. Such electron doping can weaken the ferromagnetism and
lead to a bulk band contribution in the transport measurements. Also, a larger
energy gap is required to suppress the thermal excitations for the quantum
anomalous Hall effect. Therefore, such effects can hinder the quantum anomalous
Hall state at higher temperatures. Resolving this issue can pave the way for
enhancing the observation temperature of the quantum anomalous Hall effect.
Therefore, our findings can play a significant role in the discovery of the
high-temperature quantum anomalous Hall effect in impurity-doped topological
insulators.
