  Three-dimensional topological insulators feature Dirac-like surface states
which are topologically protected against the influence of weak quenched
disorder. Here we investigate the effect of surface disorder beyond the
weak-disorder limit using large-scale numerical simulations. We find two
qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and
induces diffusive metallic behavior at the surface. Even more remarkably, for
strong surface disorder a Dirac cone reappears, as new weakly disordered
"surface" states emerge in the sample beneath the disordered surface layer,
which can be understood in terms of an interface between a topological and an
Anderson insulator. Together, this demonstrates the drastic effect of disorder
on topological surface states, which cannot be captured within effective
two-dimensional models for the surface states alone.
