  In addition to novel surface states, topological insulators can also exhibit
robust gapless states at crystalline defects. Step edges constitute a class of
common defects on the surface of crystals. In this work we establish the
topological nature of one-dimensional (1D) bound states localized at step edges
of the [001] surface of a topological crystalline insulator (TCI)
Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the
topological stability of the step edge states arises from an emergent
particle-hole symmetry of the surface low-energy physics, and demonstrate the
experimental signatures of the particle-hole symmetry breaking. We also reveal
the effects of an external magnetic field on the 1D bound states. Our work
suggests the possibility of similar topological step edge modes in other
topological materials with a rocks-salt structure.
