  Three-dimensional topological insulators are classified into "strong" (STI)
and "weak" (WTI) according to the nature of their surface states. While the
surface states of the STI are topologically protected from localization, this
does not hold for the WTI. In this work we show that the surface states of the
WTI are actually protected from any random perturbation that does not break
time-reversal symmetry, and does not close the bulk energy gap. Consequently,
the conductivity of metallic surfaces in the clean system remains finite even
in the presence of strong disorder of this type. In the weak disorder limit the
surfaces are found to be perfect metals, and strong surface disorder only acts
to push the metallic surfaces inwards. We find that the WTI differs from the
STI primarily in its anisotropy, and that the anisotropy is not a sign of its
weakness but rather of its richness.

Materials Science;Disordered Systems and Neural Networks