  In $strong$ topological insulators protected surface states are always
manifest, while in $weak$ topological insulators (WTI) the corresponding
metallic surface states are either manifest or hidden, depending on the
orientation of the surface. One can design a nanostep on the surface of WTI
such that a protected helical channel appears along it. In a more generic WTI
nanostructure, multiple sets of such quasi-1D channels emerge and are coupled
to each other. We study the response of the electronic spectrum associated with
such quasi-1D surface modes against a magnetic flux piercing the system in the
presence of disorder, and find a non-trivial, connected spectral flow as a
clear signature indicating the immunity of the surface modes to disorder. We
propose that the WTI nanoarchitecture is a promising platform for realizing
topologically protected nanocircuits immune to disorder.
