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Manipulating quantum channels in weak topological insulator nanoarchitectures

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.