Perfectly conducting channel on the dark surface of weak topological insulators

A weak topological insulator (WTI) bears, generally, an even number of Dirac cones on its surface; they are susceptible to doubling, while on the surface of a certain orientation it shows no Dirac cone. On this ``dark'' surface of a WTI, we predict that a single pair of isolated one-dimensional perfectly conducting channels emerges and forms either a closed loop or a segment of a line. The former is associated typically with a single-atomic-layer-thick island formed on the dark surface, while the latter is shown to be the consequence of a pair of crystal (screw) dislocations terminating on the dark surface.