  Quantum spin Hall insulator/metal interfaces are formed in graphene ribbons
with intrinsic spin-orbit coupling by selectively doping two regions creating a
potential step. For a clean graphene ribbon, the transmission of the
topological edge states through a n-n or p-p junction is perfect irrespective
of the ribbon termination, width, and potential step parameters due to the
orthogonality of incoming and outgoing edge channels. This is shown numerically
for an arbitrary crystallographic orientation of the ribbon and proven
analytically for zigzag and metallic armchair boundary conditions. In
disordered ribbons, the orthogonality between left- and right-movers is in
general destroyed and backscattering sets in. However, transmission approaches
one by increasing the ribbon's width, even in the presence of strong edge
roughness.
