  We explore the electronic structure and transport properties of a metal on
top of a (weakly coupled) two-dimensional topological insulator. Unlike the
widely studied junctions between topological non-trivial materials, the systems
studied here allow for a unique bandstructure and transport steering. First,
states on the topological insulator layer may coexist with the gapless bulk
and, second, the edge states on one edge can be selectively switched-off,
thereby leading to nearly perfect directional transport of charge and spin even
in the zero bias limit. We illustrate these phenomena for Bernal stacked
bilayer graphene with Haldane or intrinsic spin-orbit terms and a perpendicular
bias voltage. This opens a path for realizing directed transport in materials
such as van der Waals heterostructures, monolayer and ultrathin topological
insulators.
