  Using a generalized wave matching method we solve the full scattering problem
for quantum spin Hall insulator (QSHI) - superconductor (SC) - QSHI junctions.
We find that for systems narrow enough so that the bulk states in the SC part
couple both edges, the crossed Andreev reflection (CAR) is significant and the
electron cotunneling (T) and CAR become spatially separated. We study the
effectiveness of this separation as a function of the system geometry and the
level of doping in the SC. Moreover, we show that the spatial separation of
both effects allows for an all-electrical measurement of CAR and T separately
in a 5-terminal setup or by using the spin selection of the quantum spin Hall
effect in an H-bar structure.
