  Point-contact spectroscopy of several non-superconducting topological
materials reveals a low temperature phase transition that is characterized by a
Bardeen-Cooper-Schrieffer-type of criticality. We find such a behavior of
differential conductance for topological surfaces of non-magnetic and magnetic
Pb$_{1-y-x}$Sn$_y$Mn$_x$Te. We examine a possible contribution from
superconducting nanoparticles, and show to what extent our data are consistent
with Brzezicki's et al. theory [arXiv:1812.02168], assigning the observations
to a collective state adjacent to atomic steps at topological surfaces.
