  The outstanding transport properties expected at the edge of two-dimensional
time-reversal invariant topological insulators have proven to be challenging to
realize experimentally, and have so far only been demonstrated in very short
devices. In search for an explanation to this puzzling observation, we here
report a full first-principles calculation of topologically protected transport
at the edge of novel quantum spin Hall insulators - specifically, Bismuth and
Antimony halides - based on the non-equilibrium Green's functions formalism.
Our calculations unravel two different scattering mechanisms that may affect
two-dimensional topological insulators, namely time-reversal symmetry breaking
at vacancy defects and inter-edge scattering mediated by multiple co-operating
impurities, possibly non-magnetic. We discuss their drastic consequences for
typical non-local transport measurements as well as strategies to mitigate
their negative impact. Finally, we provide an instructive comparison of the
transport properties of topologically protected edge states to those of the
trivial edge states in MoS$_2$ ribbons. Although we focus on a few specific
cases (in terms of materials and defect types) our results should be
representative for the general case and thus have significance beyond the
systems studied here.
