  The topology of a topological material can be encoded in its surface states.
These surface states can only be removed by a bulk topological quantum phase
transition into a trivial phase. Here we use photoemission spectroscopy to
image the formation of protected surface states in a topological insulator as
we chemically tune the system through a topological transition. Surprisingly,
we discover an exotic spin-momentum locked, gapped surface state in the trivial
phase that shares many important properties with the actual topological surface
state in anticipation of the change of topology. Using a spin-resolved
measurement, we show that apart from a surface band-gap these states develop
spin textures similar to the topological surface states well-before the
transition. Our results offer a general paradigm for understanding how surface
states in topological phases arise and are suggestive for future realizing Weyl
arcs, condensed matter supersymmetry and other fascinating phenomena in the
vicinity of topological quantum criticality.
